code: from statsmodels.compat.python import lrange
  from statsmodels.compat.platform import PLATFORM_OSX, PLATFORM_WIN
  
  from io import BytesIO
  import pickle
  import os
  import warnings
  
  import numpy as np
  from numpy.testing import (assert_almost_equal, assert_, assert_allclose,
                             assert_raises)
  import pandas as pd
  from pandas import DatetimeIndex, date_range, period_range
  import pytest
  
  from statsmodels.datasets.macrodata import load_pandas as load_macrodata_pandas
  import statsmodels.sandbox.tsa.fftarma as fa
  from statsmodels.tools.testing import assert_equal
  from statsmodels.tools.sm_exceptions import (
      ValueWarning, HessianInversionWarning)
  from statsmodels.tsa.arma_mle import Arma
  from statsmodels.tsa.arima_model import AR, ARMA, ARIMA
  from statsmodels.regression.linear_model import OLS
  from statsmodels.tsa.tests.results import results_arma, results_arima
  from statsmodels.tsa.arima_process import arma_generate_sample
  
  DECIMAL_4 = 4
  DECIMAL_3 = 3
  DECIMAL_2 = 2
  DECIMAL_1 = 1
  
  current_path = os.path.dirname(os.path.abspath(__file__))
  ydata_path = os.path.join(current_path, 'results', 'y_arma_data.csv')
  with open(ydata_path, "rb") as fd:
      y_arma = np.genfromtxt(fd, delimiter=",", skip_header=1, dtype=float)
  
  cpi_dates = period_range(start='1959q1', end='2009q3', freq='Q')
  sun_dates = period_range(start='1700', end='2008', freq='A')
  cpi_predict_dates = period_range(start='2009q3', end='2015q4', freq='Q')
  sun_predict_dates = period_range(start='2008', end='2033', freq='A')
  
  
  def test_compare_arma():
      #this is a preliminary test to compare arma_kf, arma_cond_ls and arma_cond_mle
      #the results returned by the fit methods are incomplete
      #for now without random.seed
  
      np.random.seed(9876565)
      x = fa.ArmaFft([1, -0.5], [1., 0.4], 40).generate_sample(nsample=200,
              burnin=1000)
  
      # this used kalman filter through descriptive
      #d = ARMA(x)
      #d.fit((1,1), trend='nc')
      #dres = d.res
  
      modkf = ARMA(x, (1,1))
      ##rkf = mkf.fit((1,1))
      ##rkf.params
      reskf = modkf.fit(trend='nc', disp=-1)
      dres = reskf
  
      modc = Arma(x)
      resls = modc.fit(order=(1,1))
      rescm = modc.fit_mle(order=(1,1), start_params=[0.4,0.4, 1.], disp=0)
  
      #decimal 1 corresponds to threshold of 5% difference
      #still different sign  corrcted
      #assert_almost_equal(np.abs(resls[0] / d.params), np.ones(d.params.shape), decimal=1)
      assert_almost_equal(resls[0] / dres.params, np.ones(dres.params.shape),
          decimal=1)
      #rescm also contains variance estimate as last element of params
  
      #assert_almost_equal(np.abs(rescm.params[:-1] / d.params), np.ones(d.params.shape), decimal=1)
      assert_almost_equal(rescm.params[:-1] / dres.params,
                          np.ones(dres.params.shape), decimal=1)
      #return resls[0], d.params, rescm.params
  
  
  class CheckArmaResultsMixin(object):
      """
      res2 are the results from gretl.  They are in results/results_arma.
      res1 are from statsmodels
      """
      decimal_params = DECIMAL_4
  
      def test_params(self):
          assert_almost_equal(self.res1.params, self.res2.params,
                  self.decimal_params)
  
      decimal_aic = DECIMAL_4
  
      def test_aic(self):
          assert_almost_equal(self.res1.aic, self.res2.aic, self.decimal_aic)
  
      decimal_bic = DECIMAL_4
  
      def test_bic(self):
          assert_almost_equal(self.res1.bic, self.res2.bic, self.decimal_bic)
  
      decimal_arroots = DECIMAL_4
  
      def test_arroots(self):
          assert_almost_equal(self.res1.arroots, self.res2.arroots,
                      self.decimal_arroots)
  
      decimal_maroots = DECIMAL_4
  
      def test_maroots(self):
          assert_almost_equal(self.res1.maroots, self.res2.maroots,
                      self.decimal_maroots)
  
      decimal_bse = DECIMAL_2
  
      def test_bse(self):
          assert_almost_equal(self.res1.bse, self.res2.bse, self.decimal_bse)
  
      decimal_cov_params = DECIMAL_4
  
      def test_covparams(self):
          assert_almost_equal(self.res1.cov_params(), self.res2.cov_params,
                  self.decimal_cov_params)
  
      decimal_hqic = DECIMAL_4
  
      def test_hqic(self):
          assert_almost_equal(self.res1.hqic, self.res2.hqic, self.decimal_hqic)
  
      decimal_llf = DECIMAL_4
  
      def test_llf(self):
          assert_almost_equal(self.res1.llf, self.res2.llf, self.decimal_llf)
  
      decimal_resid = DECIMAL_4
  
      def test_resid(self):
          assert_almost_equal(self.res1.resid, self.res2.resid,
                  self.decimal_resid)
  
      decimal_fittedvalues = DECIMAL_4
  
      def test_fittedvalues(self):
          assert_almost_equal(self.res1.fittedvalues, self.res2.fittedvalues,
                  self.decimal_fittedvalues)
  
      decimal_pvalues = DECIMAL_2
  
      def test_pvalues(self):
          assert_almost_equal(self.res1.pvalues, self.res2.pvalues,
                      self.decimal_pvalues)
  
      decimal_t = DECIMAL_2 # only 2 decimal places in gretl output
  
      def test_tvalues(self):
          assert_almost_equal(self.res1.tvalues, self.res2.tvalues,
                              self.decimal_t)
  
      decimal_sigma2 = DECIMAL_4
  
      def test_sigma2(self):
          assert_almost_equal(self.res1.sigma2, self.res2.sigma2,
                  self.decimal_sigma2)
  
      @pytest.mark.smoke
      def test_summary(self):
          self.res1.summary()
  
  
  class CheckForecastMixin(object):
      decimal_forecast = DECIMAL_4
  
      def test_forecast(self):
          assert_almost_equal(self.res1.forecast_res, self.res2.forecast,
                  self.decimal_forecast)
  
      decimal_forecasterr = DECIMAL_4
  
      def test_forecasterr(self):
          assert_almost_equal(self.res1.forecast_err, self.res2.forecasterr,
                  self.decimal_forecasterr)
  
  
  class CheckDynamicForecastMixin(object):
      decimal_forecast_dyn = 4
  
      def test_dynamic_forecast(self):
          assert_almost_equal(self.res1.forecast_res_dyn, self.res2.forecast_dyn,
                              self.decimal_forecast_dyn)
  
      def test_forecasterr(self):
          assert_almost_equal(self.res1.forecast_err_dyn,
                              self.res2.forecasterr_dyn,
                              DECIMAL_4)
  
  
  class CheckArimaResultsMixin(CheckArmaResultsMixin):
      def test_order(self):
          assert self.res1.k_diff == self.res2.k_diff
          assert self.res1.k_ar == self.res2.k_ar
          assert self.res1.k_ma == self.res2.k_ma
  
      decimal_predict_levels = DECIMAL_4
  
      def test_predict_levels(self):
          assert_almost_equal(self.res1.predict(typ='levels'), self.res2.linear,
                  self.decimal_predict_levels)
  
  
  class Test_Y_ARMA11_NoConst(CheckArmaResultsMixin, CheckForecastMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,0]
          cls.res1 = ARMA(endog, order=(1,1)).fit(trend='nc', disp=-1)
          (cls.res1.forecast_res, cls.res1.forecast_err,
                  confint) = cls.res1.forecast(10)
          cls.res2 = results_arma.Y_arma11()
  
      def test_pickle(self):
          fh = BytesIO()
          #test wrapped results load save pickle
          self.res1.save(fh)
          fh.seek(0,0)
          res_unpickled = self.res1.__class__.load(fh)
          assert type(res_unpickled) is type(self.res1)  # noqa: E721
  
  
  class Test_Y_ARMA14_NoConst(CheckArmaResultsMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,1]
          cls.res1 = ARMA(endog, order=(1,4)).fit(trend='nc', disp=-1)
          cls.res2 = results_arma.Y_arma14()
  
  
  @pytest.mark.slow
  class Test_Y_ARMA41_NoConst(CheckArmaResultsMixin, CheckForecastMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,2]
          cls.res1 = ARMA(endog, order=(4,1)).fit(trend='nc', disp=-1)
          (cls.res1.forecast_res, cls.res1.forecast_err,
                  confint) = cls.res1.forecast(10)
          cls.res2 = results_arma.Y_arma41()
          cls.decimal_maroots = DECIMAL_3
  
  
  class Test_Y_ARMA22_NoConst(CheckArmaResultsMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,3]
          cls.res1 = ARMA(endog, order=(2,2)).fit(trend='nc', disp=-1)
          cls.res2 = results_arma.Y_arma22()
  
  
  class Test_Y_ARMA50_NoConst(CheckArmaResultsMixin, CheckForecastMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,4]
          cls.res1 = ARMA(endog, order=(5,0)).fit(trend='nc', disp=-1)
          (cls.res1.forecast_res, cls.res1.forecast_err,
                  confint) = cls.res1.forecast(10)
          cls.res2 = results_arma.Y_arma50()
  
  
  class Test_Y_ARMA02_NoConst(CheckArmaResultsMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,5]
          cls.res1 = ARMA(endog, order=(0,2)).fit(trend='nc', disp=-1)
          cls.res2 = results_arma.Y_arma02()
  
  
  class Test_Y_ARMA11_Const(CheckArmaResultsMixin, CheckForecastMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,6]
          cls.res1 = ARMA(endog, order=(1,1)).fit(trend="c", disp=-1)
          (cls.res1.forecast_res, cls.res1.forecast_err,
                  confint) = cls.res1.forecast(10)
          cls.res2 = results_arma.Y_arma11c()
  
  
  class Test_Y_ARMA14_Const(CheckArmaResultsMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,7]
          cls.res1 = ARMA(endog, order=(1,4)).fit(trend="c", disp=-1)
          cls.res2 = results_arma.Y_arma14c()
  
  
  class Test_Y_ARMA41_Const(CheckArmaResultsMixin, CheckForecastMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,8]
          cls.res2 = results_arma.Y_arma41c()
          cls.res1 = ARMA(endog, order=(4,1)).fit(trend="c", disp=-1,
                                                  start_params=cls.res2.params)
          (cls.res1.forecast_res, cls.res1.forecast_err,
                  confint) = cls.res1.forecast(10)
          cls.decimal_cov_params = DECIMAL_3
          cls.decimal_fittedvalues = DECIMAL_3
          cls.decimal_resid = DECIMAL_3
          cls.decimal_params = DECIMAL_3
  
  
  class Test_Y_ARMA22_Const(CheckArmaResultsMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,9]
          cls.res1 = ARMA(endog, order=(2,2)).fit(trend="c", disp=-1)
          cls.res2 = results_arma.Y_arma22c()
  
      def test_summary(self):
          # regression test for html of roots table #4434
          # we ignore whitespace in the assert
          summ = self.res1.summary()
          summ_roots = """\
          <tableclass="simpletable">
          <caption>Roots</caption>
          <tr>
          <td></td><th>Real</th><th>Imaginary</th><th>Modulus</th><th>Frequency</th>
          </tr>
          <tr>
          <th>AR.1</th><td>1.0991</td><td>-1.2571j</td><td>1.6698</td><td>-0.1357</td>
          </tr>
          <tr>
          <th>AR.2</th><td>1.0991</td><td>+1.2571j</td><td>1.6698</td><td>0.1357</td>
          </tr>
          <tr>
          <th>MA.1</th><td>-1.1702</td><td>+0.0000j</td><td>1.1702</td><td>0.5000</td>
          </tr>
          <tr>
          <th>MA.2</th><td>1.2215</td><td>+0.0000j</td><td>1.2215</td><td>0.0000</td>
          </tr>
          </table>"""
          assert_equal(summ.tables[2]._repr_html_().replace(' ', ''),
                       summ_roots.replace(' ', ''))
  
  
  class Test_Y_ARMA50_Const(CheckArmaResultsMixin, CheckForecastMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,10]
          cls.res1 = ARMA(endog, order=(5,0)).fit(trend="c", disp=-1)
          (cls.res1.forecast_res, cls.res1.forecast_err,
                  confint) = cls.res1.forecast(10)
          cls.res2 = results_arma.Y_arma50c()
  
  
  class Test_Y_ARMA02_Const(CheckArmaResultsMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,11]
          cls.res1 = ARMA(endog, order=(0,2)).fit(trend="c", disp=-1)
          cls.res2 = results_arma.Y_arma02c()
  
  
  # cov_params and tvalues are off still but not as much vs. R
  class Test_Y_ARMA11_NoConst_CSS(CheckArmaResultsMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,0]
          cls.res1 = ARMA(endog, order=(1,1)).fit(method="css", trend='nc',
                              disp=-1)
          cls.res2 = results_arma.Y_arma11("css")
          cls.decimal_t = DECIMAL_1
  
  
  # better vs. R
  class Test_Y_ARMA14_NoConst_CSS(CheckArmaResultsMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,1]
          cls.res1 = ARMA(endog, order=(1,4)).fit(method="css", trend='nc',
                              disp=-1)
          cls.res2 = results_arma.Y_arma14("css")
          cls.decimal_fittedvalues = DECIMAL_3
          cls.decimal_resid = DECIMAL_3
          cls.decimal_t = DECIMAL_1
  
  
  # bse, etc. better vs. R
  # maroot is off because maparams is off a bit (adjust tolerance?)
  class Test_Y_ARMA41_NoConst_CSS(CheckArmaResultsMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,2]
          cls.res1 = ARMA(endog, order=(4,1)).fit(method="css", trend='nc',
                          disp=-1)
          cls.res2 = results_arma.Y_arma41("css")
          cls.decimal_t = DECIMAL_1
          cls.decimal_pvalues = 0
          cls.decimal_cov_params = DECIMAL_3
          cls.decimal_maroots = DECIMAL_1
  
  
  #same notes as above
  class Test_Y_ARMA22_NoConst_CSS(CheckArmaResultsMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,3]
          cls.res1 = ARMA(endog, order=(2,2)).fit(method="css", trend='nc',
                              disp=-1)
          cls.res2 = results_arma.Y_arma22("css")
          cls.decimal_t = DECIMAL_1
          cls.decimal_resid = DECIMAL_3
          cls.decimal_pvalues = DECIMAL_1
          cls.decimal_fittedvalues = DECIMAL_3
  
  
  #NOTE: gretl just uses least squares for AR CSS
  # so BIC, etc. is
  # -2*res1.llf + np.log(nobs)*(res1.q+res1.p+res1.k)
  # with no adjustment for p and no extra sigma estimate
  #NOTE: so our tests use x-12 arima results which agree with us and are
  # consistent with the rest of the models
  class Test_Y_ARMA50_NoConst_CSS(CheckArmaResultsMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,4]
          cls.res1 = ARMA(endog, order=(5,0)).fit(method="css", trend='nc',
                              disp=-1)
          cls.res2 = results_arma.Y_arma50("css")
          cls.decimal_t = 0
          cls.decimal_llf = DECIMAL_1 # looks like rounding error?
  
  
  class Test_Y_ARMA02_NoConst_CSS(CheckArmaResultsMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,5]
          cls.res1 = ARMA(endog, order=(0,2)).fit(method="css", trend='nc',
                              disp=-1)
          cls.res2 = results_arma.Y_arma02("css")
  
  
  #NOTE: our results are close to --x-12-arima option and R
  class Test_Y_ARMA11_Const_CSS(CheckArmaResultsMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,6]
          cls.res1 = ARMA(endog, order=(1,1)).fit(trend="c", method="css",
                          disp=-1)
          cls.res2 = results_arma.Y_arma11c("css")
          cls.decimal_params = DECIMAL_3
          cls.decimal_cov_params = DECIMAL_3
          cls.decimal_t = DECIMAL_1
  
  
  class Test_Y_ARMA14_Const_CSS(CheckArmaResultsMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,7]
          cls.res1 = ARMA(endog, order=(1,4)).fit(trend="c", method="css",
                          disp=-1)
          cls.res2 = results_arma.Y_arma14c("css")
          cls.decimal_t = DECIMAL_1
          cls.decimal_pvalues = DECIMAL_1
  
  
  class Test_Y_ARMA41_Const_CSS(CheckArmaResultsMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,8]
          cls.res1 = ARMA(endog, order=(4,1)).fit(trend="c", method="css",
                          disp=-1)
          cls.res2 = results_arma.Y_arma41c("css")
          cls.decimal_t = DECIMAL_1
          cls.decimal_cov_params = DECIMAL_1
          cls.decimal_maroots = DECIMAL_3
          cls.decimal_bse = DECIMAL_1
  
  
  class Test_Y_ARMA22_Const_CSS(CheckArmaResultsMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,9]
          cls.res1 = ARMA(endog, order=(2,2)).fit(trend="c", method="css",
                          disp=-1)
          cls.res2 = results_arma.Y_arma22c("css")
          cls.decimal_t = 0
          cls.decimal_pvalues = DECIMAL_1
  
  
  class Test_Y_ARMA50_Const_CSS(CheckArmaResultsMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,10]
          cls.res1 = ARMA(endog, order=(5,0)).fit(trend="c", method="css",
                          disp=-1)
          cls.res2 = results_arma.Y_arma50c("css")
          cls.decimal_t = DECIMAL_1
          cls.decimal_params = DECIMAL_3
          cls.decimal_cov_params = DECIMAL_2
  
  
  class Test_Y_ARMA02_Const_CSS(CheckArmaResultsMixin):
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,11]
          cls.res1 = ARMA(endog, order=(0,2)).fit(trend="c", method="css",
                          disp=-1)
          cls.res2 = results_arma.Y_arma02c("css")
  
  
  def test_reset_trend():
      endog = y_arma[:,0]
      mod = ARMA(endog, order=(1,1))
      res1 = mod.fit(trend="c", disp=-1)
      res2 = mod.fit(trend="nc", disp=-1)
      assert_equal(len(res1.params), len(res2.params)+1)
  
  
  @pytest.mark.slow
  def test_start_params_bug():
      data = np.array([1368., 1187, 1090, 1439, 2362, 2783, 2869, 2512, 1804,
      1544, 1028, 869, 1737, 2055, 1947, 1618, 1196, 867, 997, 1862, 2525,
      3250, 4023, 4018, 3585, 3004, 2500, 2441, 2749, 2466, 2157, 1847, 1463,
      1146, 851, 993, 1448, 1719, 1709, 1455, 1950, 1763, 2075, 2343, 3570,
      4690, 3700, 2339, 1679, 1466, 998, 853, 835, 922, 851, 1125, 1299, 1105,
      860, 701, 689, 774, 582, 419, 846, 1132, 902, 1058, 1341, 1551, 1167,
      975, 786, 759, 751, 649, 876, 720, 498, 553, 459, 543, 447, 415, 377,
      373, 324, 320, 306, 259, 220, 342, 558, 825, 994, 1267, 1473, 1601,
      1896, 1890, 2012, 2198, 2393, 2825, 3411, 3406, 2464, 2891, 3685, 3638,
      3746, 3373, 3190, 2681, 2846, 4129, 5054, 5002, 4801, 4934, 4903, 4713,
      4745, 4736, 4622, 4642, 4478, 4510, 4758, 4457, 4356, 4170, 4658, 4546,
      4402, 4183, 3574, 2586, 3326, 3948, 3983, 3997, 4422, 4496, 4276, 3467,
      2753, 2582, 2921, 2768, 2789, 2824, 2482, 2773, 3005, 3641, 3699, 3774,
      3698, 3628, 3180, 3306, 2841, 2014, 1910, 2560, 2980, 3012, 3210, 3457,
      3158, 3344, 3609, 3327, 2913, 2264, 2326, 2596, 2225, 1767, 1190, 792,
      669, 589, 496, 354, 246, 250, 323, 495, 924, 1536, 2081, 2660, 2814, 2992,
      3115, 2962, 2272, 2151, 1889, 1481, 955, 631, 288, 103, 60, 82, 107, 185,
      618, 1526, 2046, 2348, 2584, 2600, 2515, 2345, 2351, 2355, 2409, 2449,
      2645, 2918, 3187, 2888, 2610, 2740, 2526, 2383, 2936, 2968, 2635, 2617,
      2790, 3906, 4018, 4797, 4919, 4942, 4656, 4444, 3898, 3908, 3678, 3605,
      3186, 2139, 2002, 1559, 1235, 1183, 1096, 673, 389, 223, 352, 308, 365,
      525, 779, 894, 901, 1025, 1047, 981, 902, 759, 569, 519, 408, 263, 156,
      72, 49, 31, 41, 192, 423, 492, 552, 564, 723, 921, 1525, 2768, 3531, 3824,
      3835, 4294, 4533, 4173, 4221, 4064, 4641, 4685, 4026, 4323, 4585, 4836,
      4822, 4631, 4614, 4326, 4790, 4736, 4104, 5099, 5154, 5121, 5384, 5274,
      5225, 4899, 5382, 5295, 5349, 4977, 4597, 4069, 3733, 3439, 3052, 2626,
      1939, 1064, 713, 916, 832, 658, 817, 921, 772, 764, 824, 967, 1127, 1153,
      824, 912, 957, 990, 1218, 1684, 2030, 2119, 2233, 2657, 2652, 2682, 2498,
      2429, 2346, 2298, 2129, 1829, 1816, 1225, 1010, 748, 627, 469, 576, 532,
      475, 582, 641, 605, 699, 680, 714, 670, 666, 636, 672, 679, 446, 248, 134,
      160, 178, 286, 413, 676, 1025, 1159, 952, 1398, 1833, 2045, 2072, 1798,
      1799, 1358, 727, 353, 347, 844, 1377, 1829, 2118, 2272, 2745, 4263, 4314,
      4530, 4354, 4645, 4547, 5391, 4855, 4739, 4520, 4573, 4305, 4196, 3773,
      3368, 2596, 2596, 2305, 2756, 3747, 4078, 3415, 2369, 2210, 2316, 2263,
      2672, 3571, 4131, 4167, 4077, 3924, 3738, 3712, 3510, 3182, 3179, 2951,
      2453, 2078, 1999, 2486, 2581, 1891, 1997, 1366, 1294, 1536, 2794, 3211,
      3242, 3406, 3121, 2425, 2016, 1787, 1508, 1304, 1060, 1342, 1589, 2361,
      3452, 2659, 2857, 3255, 3322, 2852, 2964, 3132, 3033, 2931, 2636, 2818,
      3310, 3396, 3179, 3232, 3543, 3759, 3503, 3758, 3658, 3425, 3053, 2620,
      1837, 923, 712, 1054, 1376, 1556, 1498, 1523, 1088, 728, 890, 1413, 2524,
      3295, 4097, 3993, 4116, 3874, 4074, 4142, 3975, 3908, 3907, 3918, 3755,
      3648, 3778, 4293, 4385, 4360, 4352, 4528, 4365, 3846, 4098, 3860, 3230,
      2820, 2916, 3201, 3721, 3397, 3055, 2141, 1623, 1825, 1716, 2232, 2939,
      3735, 4838, 4560, 4307, 4975, 5173, 4859, 5268, 4992, 5100, 5070, 5270,
      4760, 5135, 5059, 4682, 4492, 4933, 4737, 4611, 4634, 4789, 4811, 4379,
      4689, 4284, 4191, 3313, 2770, 2543, 3105, 2967, 2420, 1996, 2247, 2564,
      2726, 3021, 3427, 3509, 3759, 3324, 2988, 2849, 2340, 2443, 2364, 1252,
      623, 742, 867, 684, 488, 348, 241, 187, 279, 355, 423, 678, 1375, 1497,
      1434, 2116, 2411, 1929, 1628, 1635, 1609, 1757, 2090, 2085, 1790, 1846,
      2038, 2360, 2342, 2401, 2920, 3030, 3132, 4385, 5483, 5865, 5595, 5485,
      5727, 5553, 5560, 5233, 5478, 5159, 5155, 5312, 5079, 4510, 4628, 4535,
      3656, 3698, 3443, 3146, 2562, 2304, 2181, 2293, 1950, 1930, 2197, 2796,
      3441, 3649, 3815, 2850, 4005, 5305, 5550, 5641, 4717, 5131, 2831, 3518,
      3354, 3115, 3515, 3552, 3244, 3658, 4407, 4935, 4299, 3166, 3335, 2728,
      2488, 2573, 2002, 1717, 1645, 1977, 2049, 2125, 2376, 2551, 2578, 2629,
      2750, 3150, 3699, 4062, 3959, 3264, 2671, 2205, 2128, 2133, 2095, 1964,
      2006, 2074, 2201, 2506, 2449, 2465, 2064, 1446, 1382, 983, 898, 489, 319,
      383, 332, 276, 224, 144, 101, 232, 429, 597, 750, 908, 960, 1076, 951,
      1062, 1183, 1404, 1391, 1419, 1497, 1267, 963, 682, 777, 906, 1149, 1439,
      1600, 1876, 1885, 1962, 2280, 2711, 2591, 2411])
      with warnings.catch_warnings():
          warnings.simplefilter("ignore")
          res = ARMA(data, order=(4,1)).fit(start_ar_lags=5, disp=-1)
  
  
  class Test_ARIMA101(CheckArmaResultsMixin):
      # just make sure this works
      @classmethod
      def setup_class(cls):
          endog = y_arma[:,6]
          cls.res1 = ARIMA(endog, (1,0,1)).fit(trend="c", disp=-1)
          (cls.res1.forecast_res, cls.res1.forecast_err,
                  confint) = cls.res1.forecast(10)
          cls.res2 = results_arma.Y_arma11c()
          cls.res2.k_diff = 0
          cls.res2.k_ar = 1
          cls.res2.k_ma = 1
  
  
  class Test_ARIMA111(CheckArimaResultsMixin, CheckForecastMixin,
                      CheckDynamicForecastMixin):
      @classmethod
      def setup_class(cls):
          cpi = load_macrodata_pandas().data['cpi'].values
          cls.res1 = ARIMA(cpi, (1,1,1)).fit(disp=-1)
          cls.res2 = results_arima.ARIMA111()
          # make sure endog names changes to D.cpi
          cls.decimal_llf = 3
          cls.decimal_aic = 3
          cls.decimal_bic = 3
          cls.decimal_cov_params = 2 # this used to be better?
          cls.decimal_t = 0
          (cls.res1.forecast_res,
           cls.res1.forecast_err,
           conf_int)              = cls.res1.forecast(25)
          #cls.res1.forecast_res_dyn = cls.res1.predict(start=164, end=226, typ='levels', dynamic=True)
          #TODO: fix the indexing for the end here, I do not think this is right
          # if we're going to treat it like indexing
          # the forecast from 2005Q1 through 2009Q4 is indices
          # 184 through 227 not 226
          # note that the first one counts in the count so 164 + 64 is 65
          # predictions
          cls.res1.forecast_res_dyn = cls.res1.predict(start=164, end=164+63,
                                              typ='levels', dynamic=True)
  
      def test_freq(self):
          assert_almost_equal(self.res1.arfreq, [0.0000], 4)
          assert_almost_equal(self.res1.mafreq, [0.0000], 4)
  
  
  class Test_ARIMA111CSS(CheckArimaResultsMixin, CheckForecastMixin,
                         CheckDynamicForecastMixin):
      @classmethod
      def setup_class(cls):
          cpi = load_macrodata_pandas().data['cpi'].values
          cls.res1 = ARIMA(cpi, (1,1,1)).fit(disp=-1, method='css')
          cls.res2 = results_arima.ARIMA111(method='css')
          cls.res2.fittedvalues = - cpi[1:-1] + cls.res2.linear
          # make sure endog names changes to D.cpi
          (cls.res1.forecast_res,
           cls.res1.forecast_err,
           conf_int)              = cls.res1.forecast(25)
          cls.decimal_forecast = 2
          cls.decimal_forecast_dyn = 2
          cls.decimal_forecasterr = 3
          cls.res1.forecast_res_dyn = cls.res1.predict(start=164, end=164+63,
                                                   typ='levels', dynamic=True)
  
          # precisions
          cls.decimal_arroots = 3
          cls.decimal_cov_params = 3
          cls.decimal_hqic = 3
          cls.decimal_maroots = 3
          cls.decimal_t = 1
          cls.decimal_fittedvalues = 2 # because of rounding when copying
          cls.decimal_resid = 2
          #cls.decimal_llf = 3
          #cls.decimal_aic = 3
          #cls.decimal_bic = 3
          cls.decimal_predict_levels = DECIMAL_2
  
  
  class Test_ARIMA112CSS(CheckArimaResultsMixin):
      @classmethod
      def setup_class(cls):
          cpi = load_macrodata_pandas().data['cpi'].values
          cls.res1 = ARIMA(cpi, (1,1,2)).fit(disp=-1, method='css',
                                  start_params = [.905322, -.692425, 1.07366,
                                                  0.172024])
          cls.res2 = results_arima.ARIMA112(method='css')
          cls.res2.fittedvalues = - cpi[1:-1] + cls.res2.linear
          # make sure endog names changes to D.cpi
          cls.decimal_llf = 3
          cls.decimal_aic = 3
          cls.decimal_bic = 3
          #(cls.res1.forecast_res,
          # cls.res1.forecast_err,
          # conf_int)              = cls.res1.forecast(25)
          #cls.res1.forecast_res_dyn = cls.res1.predict(start=164, end=226, typ='levels', dynamic=True)
          #TODO: fix the indexing for the end here, I do not think this is right
          # if we're going to treat it like indexing
          # the forecast from 2005Q1 through 2009Q4 is indices
          # 184 through 227 not 226
          # note that the first one counts in the count so 164 + 64 is 65
          # predictions
          #cls.res1.forecast_res_dyn = self.predict(start=164, end=164+63,
          #                                         typ='levels', dynamic=True)
          # since we got from gretl do not have linear prediction in differences
          cls.decimal_arroots = 3
          cls.decimal_maroots = 2
          cls.decimal_t = 1
          cls.decimal_resid = 2
          cls.decimal_fittedvalues = 3
          cls.decimal_predict_levels = DECIMAL_3
  
      def test_freq(self):
          assert_almost_equal(self.res1.arfreq, [0.5000], 4)
          assert_almost_equal(self.res1.mafreq, [0.5000, 0.5000], 4)
  
  #class Test_ARIMADates(CheckArmaResults, CheckForecast, CheckDynamicForecast):
  #    @classmethod
  #    def setup_class(cls):
  #        cpi = load_macrodata_pandas().data['cpi'].values
  #        dates = pd.date_range('1959', periods=203, freq='Q')
  #        cls.res1 = ARIMA(cpi, dates=dates, freq='Q').fit(order=(1,1,1), disp=-1)
  #        cls.res2 = results_arima.ARIMA111()
  #        # make sure endog names changes to D.cpi
  #        cls.decimal_llf = 3
  #        cls.decimal_aic = 3
  #        cls.decimal_bic = 3
  #        (cls.res1.forecast_res,
  #         cls.res1.forecast_err,
  #         conf_int)              = cls.res1.forecast(25)
  
  
  def test_arima_predict_mle_dates():
      cpi = load_macrodata_pandas().data['cpi'].values
      res1 = ARIMA(cpi, (4,1,1), dates=cpi_dates, freq='Q').fit(disp=-1)
  
      with open(current_path + '/results/results_arima_forecasts_all_mle.csv', "rb") as test_data:
          arima_forecasts = np.genfromtxt(test_data, delimiter=",", skip_header=1, dtype=float)
  
      fc = arima_forecasts[:,0]
      fcdyn = arima_forecasts[:,1]
      fcdyn2 = arima_forecasts[:,2]
  
      start, end = 2, 51
      fv = res1.predict('1959Q3', '1971Q4', typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      assert_equal(res1.data.predict_dates, cpi_dates[start:end+1])
  
      start, end = 202, 227
      fv = res1.predict('2009Q3', '2015Q4', typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      assert_equal(res1.data.predict_dates, cpi_predict_dates)
  
      # make sure dynamic works
  
      start, end = '1960q2', '1971q4'
      fv = res1.predict(start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn[5:51+1], DECIMAL_4)
  
      start, end = '1965q1', '2015q4'
      fv = res1.predict(start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn2[24:227+1], DECIMAL_4)
  
  
  def test_arma_predict_mle_dates():
      from statsmodels.datasets.sunspots import load_pandas
      sunspots = load_pandas().data['SUNACTIVITY'].values
      mod = ARMA(sunspots, (9,0), dates=sun_dates, freq='A')
      mod.method = 'mle'
  
      assert_raises(ValueError, mod._get_prediction_index, *('1701', '1751', True))
  
      start, end = 2, 51
      _, _, _, _ = mod._get_prediction_index('1702', '1751', False)
      assert_equal(mod.data.predict_dates, sun_dates[start:end+1])
  
      start, end = 308, 333
      _, _, _, _ = mod._get_prediction_index('2008', '2033', False)
      assert_equal(mod.data.predict_dates, sun_predict_dates)
  
  
  def test_arima_predict_css_dates():
      cpi = load_macrodata_pandas().data['cpi'].values
      res1 = ARIMA(cpi, (4,1,1), dates=cpi_dates, freq='Q').fit(disp=-1,
              method='css', trend='nc')
  
      params = np.array([ 1.231272508473910,
                         -0.282516097759915,
                          0.170052755782440,
                         -0.118203728504945,
                         -0.938783134717947])
  
      with open(current_path + '/results/results_arima_forecasts_all_css.csv', "rb") as test_data:
          arima_forecasts = np.genfromtxt(test_data, delimiter=",", skip_header=1, dtype=float)
  
      fc = arima_forecasts[:,0]
      fcdyn = arima_forecasts[:,1]
      fcdyn2 = arima_forecasts[:,2]
  
      start, end = 5, 51
      fv = res1.model.predict(params, '1960Q2', '1971Q4', typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      assert_equal(res1.data.predict_dates, cpi_dates[start:end+1])
  
      start, end = 202, 227
      fv = res1.model.predict(params, '2009Q3', '2015Q4', typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      assert_equal(res1.data.predict_dates, cpi_predict_dates)
  
      # make sure dynamic works
      start, end = 5, 51
      fv = res1.model.predict(params, '1960Q2', '1971Q4', typ='levels',
                                                          dynamic=True)
      assert_almost_equal(fv, fcdyn[start:end+1], DECIMAL_4)
  
      start, end = '1965q1', '2015q4'
      fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn2[24:227+1], DECIMAL_4)
  
  
  def test_arma_predict_css_dates():
      from statsmodels.datasets.sunspots import load_pandas
      sunspots = load_pandas().data['SUNACTIVITY'].values
      mod = ARMA(sunspots, (9,0), dates=sun_dates, freq='A')
      mod.method = 'css'
      assert_raises(ValueError, mod._get_prediction_index, *('1701', '1751', False))
  
  
  def test_arima_predict_mle():
      cpi = load_macrodata_pandas().data['cpi'].values
      res1 = ARIMA(cpi, (4,1,1)).fit(disp=-1)
      # fit the model so that we get correct endog length but use
      with open(current_path + '/results/results_arima_forecasts_all_mle.csv', "rb") as test_data:
          arima_forecasts = np.genfromtxt(test_data, delimiter=",", skip_header=1, dtype=float)
      fc = arima_forecasts[:,0]
      fcdyn = arima_forecasts[:,1]
      fcdyn2 = arima_forecasts[:,2]
      fcdyn3 = arima_forecasts[:,3]
      fcdyn4 = arima_forecasts[:,4]
  
      # 0 indicates the first sample-observation below
      # ie., the index after the pre-sample, these are also differenced once
      # so the indices are moved back once from the cpi in levels
      # start < p, end <p 1959q2 - 1959q4
      start, end = 1,3
      fv = res1.predict(start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start < p, end 0 1959q3 - 1960q1
      start, end = 2, 4
      fv = res1.predict(start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start < p, end >0 1959q3 - 1971q4
      start, end = 2, 51
      fv = res1.predict(start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start < p, end nobs 1959q3 - 2009q3
      start, end = 2, 202
      fv = res1.predict(start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start < p, end >nobs 1959q3 - 2015q4
      start, end = 2, 227
      fv = res1.predict(start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start 0, end >0 1960q1 - 1971q4
      start, end = 4, 51
      fv = res1.predict(start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start 0, end nobs 1960q1 - 2009q3
      start, end = 4, 202
      fv = res1.predict(start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start 0, end >nobs 1960q1 - 2015q4
      start, end = 4, 227
      fv = res1.predict(start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start >p, end >0 1965q1 - 1971q4
      start, end = 24, 51
      fv = res1.predict(start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start >p, end nobs 1965q1 - 2009q3
      start, end = 24, 202
      fv = res1.predict(start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start >p, end >nobs 1965q1 - 2015q4
      start, end = 24, 227
      fv = res1.predict(start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start nobs, end nobs 2009q3 - 2009q3
      #NOTE: raises
      #start, end = 202, 202
      #fv = res1.predict(start, end, typ='levels')
      #assert_almost_equal(fv, [])
      # start nobs, end >nobs 2009q3 - 2015q4
      start, end = 202, 227
      fv = res1.predict(start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_3)
      # start >nobs, end >nobs 2009q4 - 2015q4
      #NOTE: this raises but should not, dynamic forecasts could start
      #one period out
      start, end = 203, 227
      fv = res1.predict(start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # defaults
      start, end = None, None
      fv = res1.predict(start, end, typ='levels')
      assert_almost_equal(fv, fc[1:203], DECIMAL_4)
  
      #### Dynamic #####
  
      # start < p, end <p 1959q2 - 1959q4
      #NOTE: should raise
      #start, end = 1,3
      #fv = res1.predict(start, end, dynamic=True, typ='levels')
      #assert_almost_equal(fv, arima_forecasts[:,15])
      # start < p, end 0 1959q3 - 1960q1
  
      #NOTE: below should raise an error
      #start, end = 2, 4
      #fv = res1.predict(start, end, dynamic=True, typ='levels')
      #assert_almost_equal(fv, fcdyn[5:end+1], DECIMAL_4)
      # start < p, end >0 1959q3 - 1971q4
      #start, end = 2, 51
      #fv = res1.predict(start, end, dynamic=True, typ='levels')
      #assert_almost_equal(fv, fcdyn[5:end+1], DECIMAL_4)
      ## start < p, end nobs 1959q3 - 2009q3
      #start, end = 2, 202
      #fv = res1.predict(start, end, dynamic=True, typ='levels')
      #assert_almost_equal(fv, fcdyn[5:end+1], DECIMAL_4)
      ## start < p, end >nobs 1959q3 - 2015q4
      #start, end = 2, 227
      #fv = res1.predict(start, end, dynamic=True, typ='levels')
      #assert_almost_equal(fv, fcdyn[5:end+1], DECIMAL_4)
      # start 0, end >0 1960q1 - 1971q4
      start, end = 5, 51
      fv = res1.predict(start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn[start:end+1], DECIMAL_4)
      # start 0, end nobs 1960q1 - 2009q3
      start, end = 5, 202
      fv = res1.predict(start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn[start:end+1], DECIMAL_4)
      # start 0, end >nobs 1960q1 - 2015q4
      start, end = 5, 227
      fv = res1.predict(start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn[start:end+1], DECIMAL_4)
      # start >p, end >0 1965q1 - 1971q4
      start, end = 24, 51
      fv = res1.predict(start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn2[start:end+1], DECIMAL_4)
      # start >p, end nobs 1965q1 - 2009q3
      start, end = 24, 202
      fv = res1.predict(start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn2[start:end+1], DECIMAL_4)
      # start >p, end >nobs 1965q1 - 2015q4
      start, end = 24, 227
      fv = res1.predict(start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn2[start:end+1], DECIMAL_4)
      # start nobs, end nobs 2009q3 - 2009q3
      start, end = 202, 202
      fv = res1.predict(start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn3[start:end+1], DECIMAL_4)
      # start nobs, end >nobs 2009q3 - 2015q4
      start, end = 202, 227
      fv = res1.predict(start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn3[start:end+1], DECIMAL_4)
      # start >nobs, end >nobs 2009q4 - 2015q4
      start, end = 203, 227
      fv = res1.predict(start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn4[start:end+1], DECIMAL_4)
      # defaults
      start, end = None, None
      fv = res1.predict(start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn[5:203], DECIMAL_4)
  
  
  def _check_start(model, given, expected, dynamic):
      start, _, _, _ = model._get_prediction_index(given, None, dynamic)
      assert_equal(start, expected)
  
  
  def _check_end(model, given, end_expect, out_of_sample_expect):
      _, end, out_of_sample, _ = model._get_prediction_index(None, given, False)
      assert_equal((end, out_of_sample), (end_expect, out_of_sample_expect))
  
  
  def test_arma_predict_indices():
      from statsmodels.datasets.sunspots import load_pandas
      sunspots = load_pandas().data['SUNACTIVITY'].values
      model = ARMA(sunspots, (9,0), dates=sun_dates, freq='A')
      model.method = 'mle'
  
      # raises - pre-sample + dynamic
      assert_raises(ValueError, model._get_prediction_index, *(0, None, True))
      assert_raises(ValueError, model._get_prediction_index, *(8, None, True))
      assert_raises(ValueError, model._get_prediction_index, *('1700', None, True))
      assert_raises(ValueError, model._get_prediction_index, *('1708', None, True))
  
      # raises - start out of sample
      # TODO: remove these, start out of sample now allowed
      # assert_raises(ValueError, model._get_prediction_index, *(311, None, True))
      # assert_raises(ValueError, model._get_prediction_index, *(311, None, False))
      # assert_raises(ValueError, model._get_prediction_index, *('2010', None, True))
      # assert_raises(ValueError, model._get_prediction_index, *('2010', None, False))
  
      # works - in-sample
      # None
      start_test_cases = [
                    # given, expected, dynamic
                    (None, 9, True),
                    # all start get moved back by k_diff
                    (9, 9, True),
                    (10, 10, True),
                    # what about end of sample start - last value is first
                    # forecast
                    (309, 309, True),
                    (308, 308, True),
                    (0, 0, False),
                    (1, 1, False),
                    (4, 4, False),
  
                    # all start get moved back by k_diff
                    ('1709', 9, True),
                    ('1710', 10, True),
                    # what about end of sample start - last value is first
                    # forecast
                    ('2008', 308, True),
                    ('2009', 309, True),
                    ('1700', 0, False),
                    ('1708', 8, False),
                    ('1709', 9, False),
                    ]
  
      for case in start_test_cases:
          _check_start(*((model,) + case))
  
      # the length of sunspot is 309, so last index is 208
      end_test_cases = [(None, 308, 0),
                        (307, 307, 0),
                        (308, 308, 0),
                        (309, 308, 1),
                        (312, 308, 4),
                        (51, 51, 0),
                        (333, 308, 25),
  
                        ('2007', 307, 0),
                        ('2008', 308, 0),
                        ('2009', 308, 1),
                        ('2012', 308, 4),
                        ('1815', 115, 0),
                        ('2033', 308, 25),
                        ]
  
      for case in end_test_cases:
          _check_end(*((model,)+case))
  
  
  def test_arima_predict_indices():
      cpi = load_macrodata_pandas().data['cpi'].values
      model = ARIMA(cpi, (4,1,1), dates=cpi_dates, freq='Q')
      model.method = 'mle'
  
      # starting indices
  
      # raises - pre-sample + dynamic
      assert_raises(ValueError, model._get_prediction_index, *(0, None, True))
      assert_raises(ValueError, model._get_prediction_index, *(4, None, True))
      assert_raises(KeyError, model._get_prediction_index, *('1959Q1', None, True))
      assert_raises(ValueError, model._get_prediction_index, *('1960Q1', None, True))
  
      # raises - index differenced away
      assert_raises(ValueError, model._get_prediction_index, *(0, None, False))
      assert_raises(KeyError, model._get_prediction_index, *('1959Q1', None, False))
  
      # raises - start out of sample
      # TODO: start out of sample is now allowed; remove this code
      # assert_raises(ValueError, model._get_prediction_index, *(204, None, True))
      # assert_raises(ValueError, model._get_prediction_index, *(204, None, False))
      # assert_raises(ValueError, model._get_prediction_index, *('2010Q1', None, True))
      # assert_raises(ValueError, model._get_prediction_index, *('2010Q1', None, False))
  
      # works - in-sample
      # None
      start_test_cases = [
                    # given, expected, dynamic
                    (None, 4, True),
                    # all start get moved back by k_diff
                    (5, 4, True),
                    (6, 5, True),
                    # what about end of sample start - last value is first
                    # forecast
                    (203, 202, True),
                    (1, 0, False),
                    (4, 3, False),
                    (5, 4, False),
                    # all start get moved back by k_diff
                    ('1960Q2', 4, True),
                    ('1960Q3', 5, True),
                    # what about end of sample start - last value is first
                    # forecast
                    ('2009Q4', 202, True),
                    ('1959Q2', 0, False),
                    ('1960Q1', 3, False),
                    ('1960Q2', 4, False),
                    ]
  
      for case in start_test_cases:
          _check_start(*((model,) + case))
  
      # check raises
      #TODO: make sure dates are passing through unmolested
      #assert_raises(ValueError, model._get_predict_end, ("2001-1-1",))
  
      # the length of diff(cpi) is 202, so last index is 201
      end_test_cases = [(None, 201, 0),
                        (201, 200, 0),
                        (202, 201, 0),
                        (203, 201, 1),
                        (204, 201, 2),
                        (51, 50, 0),
                        (164+63, 201, 25),
  
                        ('2009Q2', 200, 0),
                        ('2009Q3', 201, 0),
                        ('2009Q4', 201, 1),
                        ('2010Q1', 201, 2),
                        ('1971Q4', 50, 0),
                        ('2015Q4', 201, 25),
                        ]
  
      for case in end_test_cases:
          _check_end(*((model,)+case))
  
      # check higher k_diff
      # model.k_diff = 2
      model = ARIMA(cpi, (4,2,1), dates=cpi_dates, freq='Q')
      model.method = 'mle'
  
      # raises - pre-sample + dynamic
      assert_raises(ValueError, model._get_prediction_index, *(0, None, True))
      assert_raises(ValueError, model._get_prediction_index, *(5, None, True))
      assert_raises(KeyError, model._get_prediction_index, *('1959Q1', None, True))
      assert_raises(ValueError, model._get_prediction_index, *('1960Q1', None, True))
  
      # raises - index differenced away
      assert_raises(ValueError, model._get_prediction_index, *(1, None, False))
      assert_raises(KeyError, model._get_prediction_index, *('1959Q2', None, False))
  
      start_test_cases = [(None, 4, True),
                    # all start get moved back by k_diff
                    (6, 4, True),
                    # what about end of sample start - last value is first
                    # forecast
                    (203, 201, True),
                    (2, 0, False),
                    (4, 2, False),
                    (5, 3, False),
                    ('1960Q3', 4, True),
                    # what about end of sample start - last value is first
                    # forecast
                    ('2009Q4', 201, True),
                    ('2009Q4', 201, True),
                    ('1959Q3', 0, False),
                    ('1960Q1', 2, False),
                    ('1960Q2', 3, False),
                    ]
  
      for case in start_test_cases:
          _check_start(*((model,)+case))
  
      end_test_cases = [(None, 200, 0),
                        (201, 199, 0),
                        (202, 200, 0),
                        (203, 200, 1),
                        (204, 200, 2),
                        (51, 49, 0),
                        (164+63, 200, 25),
  
                        ('2009Q2', 199, 0),
                        ('2009Q3', 200, 0),
                        ('2009Q4', 200, 1),
                        ('2010Q1', 200, 2),
                        ('1971Q4', 49, 0),
                        ('2015Q4', 200, 25),
                        ]
  
      for case in end_test_cases:
          _check_end(*((model,)+case))
  
  
  def test_arima_predict_indices_css():
      cpi = load_macrodata_pandas().data['cpi'].values
      #NOTE: Doing no-constant for now to kick the conditional exogenous
      #issue 274 down the road
      # go ahead and git the model to set up necessary variables
      model = ARIMA(cpi, (4,1,1))
      model.method = 'css'
  
      assert_raises(ValueError, model._get_prediction_index, *(0, None, False))
      assert_raises(ValueError, model._get_prediction_index, *(0, None, True))
      assert_raises(ValueError, model._get_prediction_index, *(2, None, False))
      assert_raises(ValueError, model._get_prediction_index, *(2, None, True))
  
  
  def test_arima_predict_css():
      cpi = load_macrodata_pandas().data['cpi'].values
      #NOTE: Doing no-constant for now to kick the conditional exogenous
      #issue 274 down the road
      # go ahead and git the model to set up necessary variables
      res1 = ARIMA(cpi, (4,1,1)).fit(disp=-1, method="css",
                              trend="nc")
      # but use gretl parameters to predict to avoid precision problems
      params = np.array([ 1.231272508473910,
                         -0.282516097759915,
                         0.170052755782440,
                        -0.118203728504945,
                        -0.938783134717947])
  
      with open(current_path + '/results/results_arima_forecasts_all_css.csv', "rb") as test_data:
          arima_forecasts = np.genfromtxt(test_data, delimiter=",", skip_header=1, dtype=float)
      fc = arima_forecasts[:,0]
      fcdyn = arima_forecasts[:,1]
      fcdyn2 = arima_forecasts[:,2]
      fcdyn3 = arima_forecasts[:,3]
      fcdyn4 = arima_forecasts[:,4]
  
      #NOTE: should raise
      #start, end = 1,3
      #fv = res1.model.predict(params, start, end)
      ## start < p, end 0 1959q3 - 1960q1
      #start, end = 2, 4
      #fv = res1.model.predict(params, start, end)
      ## start < p, end >0 1959q3 - 1971q4
      #start, end = 2, 51
      #fv = res1.model.predict(params, start, end)
      ## start < p, end nobs 1959q3 - 2009q3
      #start, end = 2, 202
      #fv = res1.model.predict(params, start, end)
      ## start < p, end >nobs 1959q3 - 2015q4
      #start, end = 2, 227
      #fv = res1.model.predict(params, start, end)
      # start 0, end >0 1960q1 - 1971q4
      start, end = 5, 51
      fv = res1.model.predict(params, start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start 0, end nobs 1960q1 - 2009q3
      start, end = 5, 202
      fv = res1.model.predict(params, start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start 0, end >nobs 1960q1 - 2015q4
      #TODO: why detoriating precision?
      fv = res1.model.predict(params, start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start >p, end >0 1965q1 - 1971q4
      start, end = 24, 51
      fv = res1.model.predict(params, start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start >p, end nobs 1965q1 - 2009q3
      start, end = 24, 202
      fv = res1.model.predict(params, start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start >p, end >nobs 1965q1 - 2015q4
      start, end = 24, 227
      fv = res1.model.predict(params, start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start nobs, end nobs 2009q3 - 2009q3
      start, end = 202, 202
      fv = res1.model.predict(params, start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start nobs, end >nobs 2009q3 - 2015q4
      start, end = 202, 227
      fv = res1.model.predict(params, start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start >nobs, end >nobs 2009q4 - 2015q4
      start, end = 203, 227
      fv = res1.model.predict(params, start, end, typ='levels')
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # defaults
      start, end = None, None
      fv = res1.model.predict(params, start, end, typ='levels')
      assert_almost_equal(fv, fc[5:203], DECIMAL_4)
  
      #### Dynamic #####
  
      #NOTE: should raise
      # start < p, end <p 1959q2 - 1959q4
      #start, end = 1,3
      #fv = res1.predict(start, end, dynamic=True)
      # start < p, end 0 1959q3 - 1960q1
      #start, end = 2, 4
      #fv = res1.predict(start, end, dynamic=True)
      ## start < p, end >0 1959q3 - 1971q4
      #start, end = 2, 51
      #fv = res1.predict(start, end, dynamic=True)
      ## start < p, end nobs 1959q3 - 2009q3
      #start, end = 2, 202
      #fv = res1.predict(start, end, dynamic=True)
      ## start < p, end >nobs 1959q3 - 2015q4
      #start, end = 2, 227
      #fv = res1.predict(start, end, dynamic=True)
      # start 0, end >0 1960q1 - 1971q4
      start, end = 5, 51
      fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn[start:end+1], DECIMAL_4)
      # start 0, end nobs 1960q1 - 2009q3
      start, end = 5, 202
      fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn[start:end+1], DECIMAL_4)
      # start 0, end >nobs 1960q1 - 2015q4
      start, end = 5, 227
      fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn[start:end+1], DECIMAL_4)
      # start >p, end >0 1965q1 - 1971q4
      start, end = 24, 51
      fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn2[start:end+1], DECIMAL_4)
      # start >p, end nobs 1965q1 - 2009q3
      start, end = 24, 202
      fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn2[start:end+1], DECIMAL_4)
      # start >p, end >nobs 1965q1 - 2015q4
      start, end = 24, 227
      fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn2[start:end+1], DECIMAL_4)
      # start nobs, end nobs 2009q3 - 2009q3
      start, end = 202, 202
      fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn3[start:end+1], DECIMAL_4)
      # start nobs, end >nobs 2009q3 - 2015q4
      start, end = 202, 227
      fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
      # start >nobs, end >nobs 2009q4 - 2015q4
      start, end = 203, 227
      fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn4[start:end+1], DECIMAL_4)
      # defaults
      start, end = None, None
      fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
      assert_almost_equal(fv, fcdyn[5:203], DECIMAL_4)
  
  
  def test_arima_predict_css_diffs():
  
      cpi = load_macrodata_pandas().data['cpi'].values
      #NOTE: Doing no-constant for now to kick the conditional exogenous
      #issue 274 down the road
      # go ahead and git the model to set up necessary variables
      res1 = ARIMA(cpi, (4,1,1)).fit(disp=-1, method="css",
                              trend="c")
      # but use gretl parameters to predict to avoid precision problems
      params = np.array([0.78349893861244,
                        -0.533444105973324,
                         0.321103691668809,
                         0.264012463189186,
                         0.107888256920655,
                         0.920132542916995])
      # we report mean, should we report constant?
      params[0] = params[0] / (1 - params[1:5].sum())
  
      with open(current_path + '/results/results_arima_forecasts_all_css_diff.csv', "rb") as test_data:
          arima_forecasts = np.genfromtxt(test_data, delimiter=",", skip_header=1, dtype=float)
      fc = arima_forecasts[:,0]
      fcdyn = arima_forecasts[:,1]
      fcdyn2 = arima_forecasts[:,2]
      fcdyn3 = arima_forecasts[:,3]
      fcdyn4 = arima_forecasts[:,4]
  
      #NOTE: should raise
      #start, end = 1,3
      #fv = res1.model.predict(params, start, end)
      ## start < p, end 0 1959q3 - 1960q1
      #start, end = 2, 4
      #fv = res1.model.predict(params, start, end)
      ## start < p, end >0 1959q3 - 1971q4
      #start, end = 2, 51
      #fv = res1.model.predict(params, start, end)
      ## start < p, end nobs 1959q3 - 2009q3
      #start, end = 2, 202
      #fv = res1.model.predict(params, start, end)
      ## start < p, end >nobs 1959q3 - 2015q4
      #start, end = 2, 227
      #fv = res1.model.predict(params, start, end)
      # start 0, end >0 1960q1 - 1971q4
      start, end = 5, 51
      fv = res1.model.predict(params, start, end)
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start 0, end nobs 1960q1 - 2009q3
      start, end = 5, 202
      fv = res1.model.predict(params, start, end)
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start 0, end >nobs 1960q1 - 2015q4
      #TODO: why detoriating precision?
      fv = res1.model.predict(params, start, end)
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start >p, end >0 1965q1 - 1971q4
      start, end = 24, 51
      fv = res1.model.predict(params, start, end)
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start >p, end nobs 1965q1 - 2009q3
      start, end = 24, 202
      fv = res1.model.predict(params, start, end)
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start >p, end >nobs 1965q1 - 2015q4
      start, end = 24, 227
      fv = res1.model.predict(params, start, end)
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start nobs, end nobs 2009q3 - 2009q3
      start, end = 202, 202
      fv = res1.model.predict(params, start, end)
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start nobs, end >nobs 2009q3 - 2015q4
      start, end = 202, 227
      fv = res1.model.predict(params, start, end)
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start >nobs, end >nobs 2009q4 - 2015q4
      start, end = 203, 227
      fv = res1.model.predict(params, start, end)
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # defaults
      start, end = None, None
      fv = res1.model.predict(params, start, end)
      assert_almost_equal(fv, fc[5:203], DECIMAL_4)
  
      #### Dynamic #####
  
      #NOTE: should raise
      # start < p, end <p 1959q2 - 1959q4
      #start, end = 1,3
      #fv = res1.predict(start, end, dynamic=True)
      # start < p, end 0 1959q3 - 1960q1
      #start, end = 2, 4
      #fv = res1.predict(start, end, dynamic=True)
      ## start < p, end >0 1959q3 - 1971q4
      #start, end = 2, 51
      #fv = res1.predict(start, end, dynamic=True)
      ## start < p, end nobs 1959q3 - 2009q3
      #start, end = 2, 202
      #fv = res1.predict(start, end, dynamic=True)
      ## start < p, end >nobs 1959q3 - 2015q4
      #start, end = 2, 227
      #fv = res1.predict(start, end, dynamic=True)
      # start 0, end >0 1960q1 - 1971q4
      start, end = 5, 51
      fv = res1.model.predict(params, start, end, dynamic=True)
      assert_almost_equal(fv, fcdyn[start:end+1], DECIMAL_4)
      # start 0, end nobs 1960q1 - 2009q3
      start, end = 5, 202
      fv = res1.model.predict(params, start, end, dynamic=True)
      assert_almost_equal(fv, fcdyn[start:end+1], DECIMAL_4)
      # start 0, end >nobs 1960q1 - 2015q4
      start, end = 5, 227
      fv = res1.model.predict(params, start, end, dynamic=True)
      assert_almost_equal(fv, fcdyn[start:end+1], DECIMAL_4)
      # start >p, end >0 1965q1 - 1971q4
      start, end = 24, 51
      fv = res1.model.predict(params, start, end, dynamic=True)
      assert_almost_equal(fv, fcdyn2[start:end+1], DECIMAL_4)
      # start >p, end nobs 1965q1 - 2009q3
      start, end = 24, 202
      fv = res1.model.predict(params, start, end, dynamic=True)
      assert_almost_equal(fv, fcdyn2[start:end+1], DECIMAL_4)
      # start >p, end >nobs 1965q1 - 2015q4
      start, end = 24, 227
      fv = res1.model.predict(params, start, end, dynamic=True)
      assert_almost_equal(fv, fcdyn2[start:end+1], DECIMAL_4)
      # start nobs, end nobs 2009q3 - 2009q3
      start, end = 202, 202
      fv = res1.model.predict(params, start, end, dynamic=True)
      assert_almost_equal(fv, fcdyn3[start:end+1], DECIMAL_4)
      # start nobs, end >nobs 2009q3 - 2015q4
      start, end = 202, 227
      fv = res1.model.predict(params, start, end, dynamic=True)
      # start >nobs, end >nobs 2009q4 - 2015q4
      start, end = 203, 227
      fv = res1.model.predict(params, start, end, dynamic=True)
      assert_almost_equal(fv, fcdyn4[start:end+1], DECIMAL_4)
      # defaults
      start, end = None, None
      fv = res1.model.predict(params, start, end, dynamic=True)
      assert_almost_equal(fv, fcdyn[5:203], DECIMAL_4)
  
  
  def test_arima_predict_mle_diffs():
  
      cpi = load_macrodata_pandas().data['cpi'].values
      #NOTE: Doing no-constant for now to kick the conditional exogenous
      #issue 274 down the road
      # go ahead and git the model to set up necessary variables
      res1 = ARIMA(cpi, (4,1,1)).fit(disp=-1, trend="c")
      # but use gretl parameters to predict to avoid precision problems
      params = np.array([0.926875951549299,
          -0.555862621524846,
          0.320865492764400,
          0.252253019082800,
          0.113624958031799,
          0.939144026934634])
  
      with open(current_path + '/results/results_arima_forecasts_all_mle_diff.csv', "rb") as test_data:
          arima_forecasts = np.genfromtxt(test_data, delimiter=",", skip_header=1, dtype=float)
      fc = arima_forecasts[:,0]
      fcdyn = arima_forecasts[:,1]
      fcdyn2 = arima_forecasts[:,2]
      fcdyn3 = arima_forecasts[:,3]
      fcdyn4 = arima_forecasts[:,4]
  
      #NOTE: should raise
      start, end = 1,3
      fv = res1.model.predict(params, start, end)
      ## start < p, end 0 1959q3 - 1960q1
      start, end = 2, 4
      fv = res1.model.predict(params, start, end)
      ## start < p, end >0 1959q3 - 1971q4
      start, end = 2, 51
      fv = res1.model.predict(params, start, end)
      ## start < p, end nobs 1959q3 - 2009q3
      start, end = 2, 202
      fv = res1.model.predict(params, start, end)
      ## start < p, end >nobs 1959q3 - 2015q4
      start, end = 2, 227
      fv = res1.model.predict(params, start, end)
      # start 0, end >0 1960q1 - 1971q4
      start, end = 5, 51
      fv = res1.model.predict(params, start, end)
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start 0, end nobs 1960q1 - 2009q3
      start, end = 5, 202
      fv = res1.model.predict(params, start, end)
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start 0, end >nobs 1960q1 - 2015q4
      #TODO: why detoriating precision?
      fv = res1.model.predict(params, start, end)
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start >p, end >0 1965q1 - 1971q4
      start, end = 24, 51
      fv = res1.model.predict(params, start, end)
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start >p, end nobs 1965q1 - 2009q3
      start, end = 24, 202
      fv = res1.model.predict(params, start, end)
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start >p, end >nobs 1965q1 - 2015q4
      start, end = 24, 227
      fv = res1.model.predict(params, start, end)
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start nobs, end nobs 2009q3 - 2009q3
      start, end = 202, 202
      fv = res1.model.predict(params, start, end)
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start nobs, end >nobs 2009q3 - 2015q4
      start, end = 202, 227
      fv = res1.model.predict(params, start, end)
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # start >nobs, end >nobs 2009q4 - 2015q4
      start, end = 203, 227
      fv = res1.model.predict(params, start, end)
      assert_almost_equal(fv, fc[start:end+1], DECIMAL_4)
      # defaults
      start, end = None, None
      fv = res1.model.predict(params, start, end)
      assert_almost_equal(fv, fc[1:203], DECIMAL_4)
  
      #### Dynamic #####
  
      #NOTE: should raise
      # start < p, end <p 1959q2 - 1959q4
      #start, end = 1,3
      #fv = res1.predict(start, end, dynamic=True)
      # start < p, end 0 1959q3 - 1960q1
      #start, end = 2, 4
      #fv = res1.predict(start, end, dynamic=True)
      ## start < p, end >0 1959q3 - 1971q4
      #start, end = 2, 51
      #fv = res1.predict(start, end, dynamic=True)
      ## start < p, end nobs 1959q3 - 2009q3
      #start, end = 2, 202
      #fv = res1.predict(start, end, dynamic=True)
      ## start < p, end >nobs 1959q3 - 2015q4
      #start, end = 2, 227
      #fv = res1.predict(start, end, dynamic=True)
      # start 0, end >0 1960q1 - 1971q4
      start, end = 5, 51
      fv = res1.model.predict(params, start, end, dynamic=True)
      assert_almost_equal(fv, fcdyn[start:end+1], DECIMAL_4)
      # start 0, end nobs 1960q1 - 2009q3
      start, end = 5, 202
      fv = res1.model.predict(params, start, end, dynamic=True)
      assert_almost_equal(fv, fcdyn[start:end+1], DECIMAL_4)
      # start 0, end >nobs 1960q1 - 2015q4
      start, end = 5, 227
      fv = res1.model.predict(params, start, end, dynamic=True)
      assert_almost_equal(fv, fcdyn[start:end+1], DECIMAL_4)
      # start >p, end >0 1965q1 - 1971q4
      start, end = 24, 51
      fv = res1.model.predict(params, start, end, dynamic=True)
      assert_almost_equal(fv, fcdyn2[start:end+1], DECIMAL_4)
      # start >p, end nobs 1965q1 - 2009q3
      start, end = 24, 202
      fv = res1.model.predict(params, start, end, dynamic=True)
      assert_almost_equal(fv, fcdyn2[start:end+1], DECIMAL_4)
      # start >p, end >nobs 1965q1 - 2015q4
      start, end = 24, 227
      fv = res1.model.predict(params, start, end, dynamic=True)
      assert_almost_equal(fv, fcdyn2[start:end+1], DECIMAL_4)
      # start nobs, end nobs 2009q3 - 2009q3
      start, end = 202, 202
      fv = res1.model.predict(params, start, end, dynamic=True)
      assert_almost_equal(fv, fcdyn3[start:end+1], DECIMAL_4)
      # start nobs, end >nobs 2009q3 - 2015q4
      start, end = 202, 227
      fv = res1.model.predict(params, start, end, dynamic=True)
      # start >nobs, end >nobs 2009q4 - 2015q4
      start, end = 203, 227
      fv = res1.model.predict(params, start, end, dynamic=True)
      assert_almost_equal(fv, fcdyn4[start:end+1], DECIMAL_4)
      # defaults
      start, end = None, None
      fv = res1.model.predict(params, start, end, dynamic=True)
      assert_almost_equal(fv, fcdyn[5:203], DECIMAL_4)
  
  
  def test_arima_wrapper():
      cpi = load_macrodata_pandas().data['cpi']
      cpi.index = pd.Index(cpi_dates)
      res = ARIMA(cpi, (4,1,1), freq='Q').fit(disp=-1)
      assert_equal(res.params.index, pd.Index(['const', 'ar.L1.D.cpi', 'ar.L2.D.cpi',
                                      'ar.L3.D.cpi', 'ar.L4.D.cpi',
                                      'ma.L1.D.cpi']))
      assert_equal(res.model.endog_names, 'D.cpi')
  
  
  @pytest.mark.smoke
  def test_1dexog():
      # smoke test, this will raise an error if broken
      dta = load_macrodata_pandas().data
      endog = dta['realcons'].values
      exog = dta['m1'].values.squeeze()
      with warnings.catch_warnings():
          warnings.simplefilter("ignore")
          mod = ARMA(endog, (1,1), exog).fit(disp=-1)
          mod.predict(193, 203, exog[-10:])
  
          # check for dynamic is true and pandas Series  see #2589
          mod.predict(193, 202, exog[-10:], dynamic=True)
  
          dta.index = pd.Index(cpi_dates)
          mod = ARMA(dta['realcons'], (1,1), dta['m1']).fit(disp=-1)
          mod.predict(dta.index[-10], dta.index[-1], exog=dta['m1'][-10:], dynamic=True)
  
          mod = ARMA(dta['realcons'], (1,1), dta['m1']).fit(trend='nc', disp=-1)
          mod.predict(dta.index[-10], dta.index[-1], exog=dta['m1'][-10:], dynamic=True)
  
  
  def test_arima_predict_bug():
      #predict_start_date was not getting set on start = None
      from statsmodels.datasets import sunspots
      dta = sunspots.load_pandas().data.SUNACTIVITY
      dta.index = pd.date_range(start='1700', end='2009', freq='A')[:309]
      arma_mod20 = ARMA(dta, (2,0)).fit(disp=-1)
      arma_mod20.predict(None, None)
  
      # test prediction with time stamp, see #2587
      predict = arma_mod20.predict(dta.index[-20], dta.index[-1])
      assert_(predict.index.equals(dta.index[-20:]))
      predict = arma_mod20.predict(dta.index[-20], dta.index[-1], dynamic=True)
      assert_(predict.index.equals(dta.index[-20:]))
      # partially out of sample
      predict_dates = pd.date_range(start='2000', end='2015', freq='A')
      predict = arma_mod20.predict(predict_dates[0], predict_dates[-1])
      assert_(predict.index.equals(predict_dates))
      #assert_(1 == 0)
  
  
  def test_arima_predict_q2():
      # bug with q > 1 for arima predict
      inv = load_macrodata_pandas().data['realinv'].values
      arima_mod = ARIMA(np.log(inv), (1,1,2)).fit(start_params=[0,0,0,0], disp=-1)
      fc, stderr, conf_int = arima_mod.forecast(5)
      # values copy-pasted from gretl
      assert_almost_equal(fc,
                          [7.306320, 7.313825, 7.321749, 7.329827, 7.337962],
                          5)
  
  
  def test_arima_predict_pandas_nofreq():
      # this is issue 712
      dates = ["2010-01-04", "2010-01-05", "2010-01-06", "2010-01-07",
               "2010-01-08", "2010-01-11", "2010-01-12", "2010-01-11",
               "2010-01-12", "2010-01-13", "2010-01-17"]
      close = [626.75, 623.99, 608.26, 594.1, 602.02, 601.11, 590.48, 587.09,
               589.85, 580.0,587.62]
      data = pd.DataFrame(close, index=DatetimeIndex(dates), columns=["close"])
  
      # TODO: fix this names bug for non-string names names
      with pytest.warns(ValueWarning, match="it has no associated frequency"):
          arma = ARMA(data, order=(1, 0)).fit(disp=-1)
  
      # first check that in-sample prediction works
      predict = arma.predict()
  
      assert_(predict.index.equals(data.index))
  
      # check that this raises an exception when date not on index
      assert_raises(KeyError, arma.predict, start="2010-1-9", end=10)
      assert_raises(KeyError, arma.predict, start="2010-1-9", end="2010-1-17")
  
      # raise because end not on index
      assert_raises(KeyError, arma.predict, start="2010-1-4", end="2010-1-10")
      # raise because end not on index
      assert_raises(KeyError, arma.predict, start=3, end="2010-1-10")
  
      predict = arma.predict(start="2010-1-7", end=10) # should be of length 10
      assert_(len(predict) == 8)
      assert_(predict.index.equals(data.index[3:10+1]))
  
      with pytest.warns(ValueWarning, match="No supported index is available"):
          predict = arma.predict(start="2010-1-7", end=14)
  
      assert_(predict.index.equals(pd.Index(lrange(3, 15))))
  
      with pytest.warns(ValueWarning, match="No supported index is available"):
          predict = arma.predict(start=3, end=14)
  
      assert_(predict.index.equals(pd.Index(lrange(3, 15))))
  
      # end can be a date if it's in the sample and on the index
      # predict dates is just a slice of the dates index then
      predict = arma.predict(start="2010-1-6", end="2010-1-13")
      assert_(predict.index.equals(data.index[2:10]))
      predict = arma.predict(start=2, end="2010-1-13")
      assert_(predict.index.equals(data.index[2:10]))
  
  
  def test_arima_predict_exog():
      # check 625 and 626
      #from statsmodels.tsa.arima_process import arma_generate_sample
      #arparams = np.array([1, -.45, .25])
      #maparams = np.array([1, .15])
      #nobs = 100
      #np.random.seed(123)
      #y = arma_generate_sample(arparams, maparams, nobs, burnin=100)
  
      ## make an exogenous trend
      #X = np.array(lrange(nobs)) / 20.0
      ## add a constant
      #y += 2.5
  
      from pandas import read_csv
      arima_forecasts = read_csv(current_path + "/results/"
                              "results_arima_exog_forecasts_mle.csv")
      y = arima_forecasts["y"].dropna()
      X = np.arange(len(y) + 25)/20.
      predict_expected = arima_forecasts["predict"]
      arma_res = ARMA(y.values, order=(2,1), exog=X[:100]).fit(trend="c",
                                                               disp=-1)
      # params from gretl
      params = np.array([2.786912485145725, -0.122650190196475,
                         0.533223846028938, -0.319344321763337,
                         0.132883233000064])
      assert_almost_equal(arma_res.params, params, 5)
      # no exog for in-sample
      predict = arma_res.predict()
      assert_almost_equal(predict, predict_expected.values[:100], 5)
  
      # check 626
      assert_(len(arma_res.model.exog_names) == 5)
  
      # exog for out-of-sample and in-sample dynamic
      predict = arma_res.model.predict(params, end=124, exog=X[100:])
      assert_almost_equal(predict, predict_expected.values, 6)
  
      # conditional sum of squares
      #arima_forecasts = read_csv(current_path + "/results/"
      #                        "results_arima_exog_forecasts_css.csv")
      #predict_expected = arima_forecasts["predict"].dropna()
      #arma_res = ARMA(y.values, order=(2,1), exog=X[:100]).fit(trend="c",
      #                                                         method="css",
      #                                                         disp=-1)
  
      #params = np.array([2.152350033809826, -0.103602399018814,
      #                   0.566716580421188, -0.326208009247944,
      #                   0.102142932143421])
      #predict = arma_res.model.predict(params)
      ## in-sample
      #assert_almost_equal(predict, predict_expected.values[:98], 6)
  
      #predict = arma_res.model.predict(params, end=124, exog=X[100:])
      ## exog for out-of-sample and in-sample dynamic
      #assert_almost_equal(predict, predict_expected.values, 3)
  
  
  @pytest.mark.smoke
  def test_arima_no_diff():
      # GH#736
      # smoke test, predict will break if we have ARIMAResults but
      # ARMA model, need ARIMA(p, 0, q) to return an ARMA in init.
      ar = [1, -.75, .15, .35]
      ma = [1, .25, .9]
      np.random.seed(12345)
      y = arma_generate_sample(ar, ma, 100)
      mod = ARIMA(y, (3, 0, 2))
      assert_(type(mod) is ARMA)
      res = mod.fit(disp=-1)
      # smoke test just to be sure
      res.predict()
  
  
  @pytest.mark.smoke
  def test_arima_predict_noma():
      # GH#657
      ar = [1, .75]
      ma = [1]
      np.random.seed(12345)
      data = arma_generate_sample(ar, ma, 100)
      arma = ARMA(data, order=(0,1))
      arma_res = arma.fit(disp=-1)
      arma_res.forecast(1)
  
  
  def test_arimax():
      dta = load_macrodata_pandas().data
      dates = pd.date_range("1959", periods=len(dta), freq='Q')
      dta.index = cpi_dates
      dta = dta[["realdpi", "m1", "realgdp"]]
      y = dta.pop("realdpi")
  
      # 1 exog
      #X = dta.iloc[1:]["m1"]
      #res = ARIMA(y, (2, 1, 1), X).fit(disp=-1)
      #params = [23.902305009084373, 0.024650911502790, -0.162140641341602,
      #          0.165262136028113, -0.066667022903974]
      #assert_almost_equal(res.params.values, params, 6)
  
      # 2 exog
      X = dta
      res = ARIMA(y, (2, 1, 1), X).fit(disp=False, solver="nm", maxiter=1000,
                  ftol=1e-12, xtol=1e-12)
  
      # from gretl
      #params = [13.113976653926638, -0.003792125069387,  0.004123504809217,
      #          -0.199213760940898,  0.151563643588008, -0.033088661096699]
      # from stata using double
      stata_llf = -1076.108614859121
      params = [13.1259220104, -0.00376814509403812, 0.00411970083135622,
                -0.19921477896158524, 0.15154396192855729, -0.03308400760360837]
      # we can get close
      assert_almost_equal(res.params.values, params, 4)
  
      # This shows that it's an optimizer problem and not a problem in the code
      assert_almost_equal(res.model.loglike(np.array(params)), stata_llf, 6)
  
      X = dta.diff()
      X.iloc[0] = 0
      res = ARIMA(y, (2, 1, 1), X).fit(disp=False)
  
      # gretl will not estimate this - looks like maybe a bug on their part,
      # but we can just fine, we're close to Stata's answer
      # from Stata
      params = [19.5656863783347, 0.32653841355833396198,
                0.36286527042965188716, -1.01133792126884,
                -0.15722368379307766206, 0.69359822544092153418]
  
      assert_almost_equal(res.params.values, params, 3)
  
  
  def test_bad_start_params():
      endog = np.array([
          820.69093,      781.0103028,    785.8786988,    767.64282267,
          778.9837648,    824.6595702,    813.01877867,   751.65598567,
          753.431091,     746.920813,     795.6201904,    772.65732833,
          793.4486454,    868.8457766,    823.07226547,   783.09067747,
          791.50723847,   770.93086347,   835.34157333,   810.64147947,
          738.36071367,   776.49038513,   822.93272333,   815.26461227,
          773.70552987,   777.3726522,    811.83444853,   840.95489133,
          777.51031933,   745.90077307,   806.95113093,   805.77521973,
          756.70927733,   749.89091773,  1694.2266924,   2398.4802244,
          1434.6728516,   909.73940427,   929.01291907,   769.07561453,
          801.1112548,    796.16163313,   817.2496376,    857.73046447,
          838.849345,     761.92338873,   731.7842242,    770.4641844])
  
      mod = ARMA(endog, (15, 0))
      with pytest.raises(ValueError, match="pass your own start_params"):
          with pytest.warns(RuntimeWarning, match="encountered in sqrt"):
              # numpy warns "invalid value encountered in sqrt"
              mod.fit()
  
      inv = load_macrodata_pandas().data['realinv'].values
      arima_mod = ARIMA(np.log(inv), (1, 1, 2))
      with pytest.raises(ValueError):
          arima_mod.fit()
  
  
  def test_arima_small_data_bug():
      # Issue 1038, too few observations with given order
      import statsmodels.api as sm
  
      vals = [96.2, 98.3, 99.1, 95.5, 94.0, 87.1, 87.9, 86.7402777504474]
  
      dr = pd.date_range("1990", periods=len(vals), freq='Q')
      ts = pd.Series(vals, index=dr)
      df = pd.DataFrame(ts)
      mod = sm.tsa.ARIMA(df, (2, 0, 2))
      assert_raises(ValueError, mod.fit)
  
  
  @pytest.mark.smoke
  def test_arima_dataframe_integer_name():
      # Smoke Test for Issue GH#1038
      import statsmodels.api as sm
  
      vals = [96.2, 98.3, 99.1, 95.5, 94.0, 87.1, 87.9, 86.7402777504474,
              94.0, 96.5, 93.3, 97.5, 96.3, 92.]
  
      dr = pd.date_range("1990", periods=len(vals), freq='Q')
      ts = pd.Series(vals, index=dr)
      df = pd.DataFrame(ts)
      mod = sm.tsa.ARIMA(df, (2, 0, 2))
  
  
  def test_arima_exog_predict_1d():
      # test 1067
      np.random.seed(12345)
      y = np.random.random(100)
      x = np.random.random(100)
      mod = ARMA(y, (2, 1), x).fit(disp=-1)
      newx = np.random.random(10)
      mod.forecast(steps=10, alpha=0.05, exog=newx)
  
      with pytest.raises(ValueError):
          mod.forecast(steps=10, alpha=0.05, exog=newx[:5])
  
      with pytest.raises(ValueError):
          mod.forecast(steps=10, alpha=0.05)
  
      too_many = pd.DataFrame(np.zeros((10, 2)),
                              columns=['x1', 'x2'])
      with pytest.raises(ValueError):
          mod.forecast(steps=10, alpha=0.05, exog=too_many)
  
  
  def test_arima_1123():
      # test ARMAX predict when trend is none
      np.random.seed(12345)
      arparams = np.array([.75, -.25])
      maparams = np.array([.65, .35])
  
      arparam = np.r_[1, -arparams]
      maparam = np.r_[1, maparams]
  
      nobs = 20
  
      dates = pd.date_range(start='1980', periods=nobs, freq='A')
  
      np.random.seed(12345)
      y = arma_generate_sample(arparams, maparams, nobs)
  
      X = np.random.randn(nobs)
      y += 5*X
      mod = ARMA(y[:-1], order=(1,0), exog=X[:-1])
      res = mod.fit(trend='nc', disp=False)
      fc = res.forecast(exog=X[-1:])
      # results from gretl
      assert_almost_equal(fc[0], 2.200393, 6)
      assert_almost_equal(fc[1], 1.030743, 6)
      assert_almost_equal(fc[2][0,0], 0.180175, 6)
      assert_almost_equal(fc[2][0,1], 4.220611, 6)
  
      mod = ARMA(y[:-1], order=(1,1), exog=X[:-1])
      res = mod.fit(trend='nc', disp=False)
      fc = res.forecast(exog=X[-1:])
      assert_almost_equal(fc[0], 2.765688, 6)
      assert_almost_equal(fc[1], 0.835048, 6)
      assert_almost_equal(fc[2][0,0], 1.129023, 6)
      assert_almost_equal(fc[2][0,1], 4.402353, 6)
  
      # make sure this works to. code looked fishy.
      mod = ARMA(y[:-1], order=(1,0), exog=X[:-1])
      res = mod.fit(trend='c', disp=False)
      fc = res.forecast(exog=X[-1:])
      assert_almost_equal(fc[0], 2.481219, 6)
      assert_almost_equal(fc[1], 0.968759, 6)
      assert_almost_equal(fc[2][0], [0.582485, 4.379952], 6)
  
  
  def test_small_data():
      # 1146
      y = [-1214.360173, -1848.209905, -2100.918158, -3647.483678, -4711.186773]
  
      # refuse to estimate these
      assert_raises(ValueError, ARIMA, y, (2, 0, 3))
      assert_raises(ValueError, ARIMA, y, (1, 1, 3))
      mod = ARIMA(y, (1, 0, 3))
      assert_raises(ValueError, mod.fit, trend="c")
  
      # try to estimate these...leave it up to the user to check for garbage
      # and be clear, these are garbage parameters.
      # X-12 arima will estimate, gretl refuses to estimate likely a problem
      # in start params regression.
      res = mod.fit(trend="nc", disp=0, start_params=[.1,.1,.1,.1])
      mod = ARIMA(y, (1, 0, 2))
      import warnings
      with warnings.catch_warnings():
          warnings.simplefilter("ignore")
          res = mod.fit(disp=0, start_params=[np.mean(y), .1, .1, .1])
  
  
  class TestARMA00(object):
  
      @classmethod
      def setup_class(cls):
          from statsmodels.datasets.sunspots import load_pandas
  
          sunspots = load_pandas().data['SUNACTIVITY'].values
          cls.y = y = sunspots
          cls.arma_00_model = ARMA(y, order=(0, 0))
          cls.arma_00_res = cls.arma_00_model.fit(disp=-1)
  
      def test_parameters(self):
          params = self.arma_00_res.params
          assert_almost_equal(self.y.mean(), params)
  
      def test_predictions(self):
          predictions = self.arma_00_res.predict()
          assert_almost_equal(self.y.mean() * np.ones_like(predictions), predictions)
  
      def test_arroots(self):
          # regression test; older implementation of arroots returned None
          # instead of en empty array
          roots = self.arma_00_res.arroots
          assert_equal(roots.size, 0)
  
      def test_maroots(self):
          # regression test; older implementation of arroots returned None
          # instead of en empty array
          roots = self.arma_00_res.maroots
          assert_equal(roots.size, 0)
  
      @pytest.mark.skip("This test is invalid since the ICs differ due to "
                        "df_model differences between OLS and ARIMA")
      def test_information_criteria(self):
          res = self.arma_00_res
          y = self.y
          ols_res = OLS(y, np.ones_like(y)).fit(disp=-1)
          ols_ic = np.array([ols_res.aic, ols_res.bic])
          arma_ic = np.array([res.aic, res.bic])
          assert_almost_equal(ols_ic, arma_ic, DECIMAL_4)
  
      def test_arma_00_nc(self):
          arma_00 = ARMA(self.y, order=(0, 0))
          assert_raises(ValueError, arma_00.fit, trend='nc', disp=-1)
  
      def test_css(self):
          arma = ARMA(self.y, order=(0, 0))
          fit = arma.fit(method='css', disp=-1)
          predictions = fit.predict()
          assert_almost_equal(self.y.mean() * np.ones_like(predictions), predictions)
  
      def test_arima(self):
          yi = np.cumsum(self.y)
          arima = ARIMA(yi, order=(0, 1, 0))
          fit = arima.fit(disp=-1)
          assert_almost_equal(np.diff(yi).mean(), fit.params, DECIMAL_4)
  
      def test_arma_ols(self):
          y = self.y
          y_lead = y[1:]
          y_lag = y[:-1]
          T = y_lag.shape[0]
          X = np.hstack((np.ones((T,1)), y_lag[:,None]))
          ols_res = OLS(y_lead, X).fit()
          arma_res = ARMA(y_lead,order=(0,0),exog=y_lag).fit(trend='c', disp=-1)
          assert_almost_equal(ols_res.params, arma_res.params)
  
      def test_arma_exog_no_constant(self):
          y = self.y
          y_lead = y[1:]
          y_lag = y[:-1]
          X = y_lag[:,None]
          ols_res = OLS(y_lead, X).fit()
          arma_res = ARMA(y_lead,order=(0,0),exog=y_lag).fit(trend='nc', disp=-1)
          assert_almost_equal(ols_res.params, arma_res.params)
  
  
  def test_arima_dates_startatend():
      # bug
      np.random.seed(18)
      x = pd.Series(np.random.random(36),
                    index=pd.date_range(start='1/1/1990',
                                        periods=36, freq='M'))
      res = ARIMA(x, (1, 0, 0)).fit(disp=0)
      pred = res.predict(start=len(x), end=len(x))
      assert_(pred.index[0] == x.index.shift(1)[-1])
      fc = res.forecast()[0]
      assert_almost_equal(pred.values[0], fc)
  
  
  def test_arma_missing():
      from statsmodels.tools.sm_exceptions import MissingDataError
      # bug 1343
      y = np.random.random(40)
      y[-1] = np.nan
      assert_raises(MissingDataError, ARMA, y, (1, 0), missing='raise')
  
  
  @pytest.mark.matplotlib
  def test_plot_predict(close_figures):
      from statsmodels.datasets.sunspots import load_pandas
  
      dta = load_pandas().data[['SUNACTIVITY']]
      dta.index = date_range(start='1700', end='2009', freq='A')[:309]
      res = ARMA(dta, (3, 0)).fit(disp=-1)
      fig = res.plot_predict('1990', '2012', dynamic=True, plot_insample=False)
  
      res = ARIMA(dta, (3, 1, 0)).fit(disp=-1)
      fig = res.plot_predict('1990', '2012', dynamic=True, plot_insample=False)
  
  
  def test_arima_diff2():
      dta = load_macrodata_pandas().data['cpi']
      dates = pd.date_range("1959", periods=len(dta), freq='Q')
      dta.index = cpi_dates
      mod = ARIMA(dta, (3, 2, 1)).fit(disp=-1)
      fc, fcerr, conf_int = mod.forecast(10)
      # forecasts from gretl
      conf_int_res = [ (216.139,  219.231),
                       (216.472,  221.520),
                       (217.064,  223.649),
                       (217.586,  225.727),
                       (218.119,  227.770),
                       (218.703,  229.784),
                       (219.306,  231.777),
                       (219.924,  233.759),
                       (220.559,  235.735),
                       (221.206,  237.709)]
  
      fc_res = [217.685, 218.996, 220.356, 221.656, 222.945, 224.243, 225.541,
            226.841, 228.147, 229.457]
      fcerr_res = [0.7888, 1.2878, 1.6798, 2.0768,  2.4620, 2.8269, 3.1816,
                   3.52950, 3.8715, 4.2099]
  
      assert_almost_equal(fc, fc_res, 3)
      assert_almost_equal(fcerr, fcerr_res, 3)
      assert_almost_equal(conf_int, conf_int_res, 3)
  
      predicted = mod.predict('2008Q1', '2012Q1', typ='levels')
  
      predicted_res = [214.464, 215.478, 221.277, 217.453, 212.419, 213.530,
                       215.087, 217.685 , 218.996 , 220.356 , 221.656 ,
                       222.945 , 224.243 , 225.541 , 226.841 , 228.147 ,
                       229.457]
      assert_almost_equal(predicted, predicted_res, 3)
  
  
  def test_arima111_predict_exog_2127():
      # regression test for issue #2127
      ef = [0.03005, 0.03917, 0.02828, 0.03644, 0.03379, 0.02744,
            0.03343, 0.02621, 0.03050, 0.02455, 0.03261, 0.03507,
            0.02734, 0.05373, 0.02677, 0.03443, 0.03331, 0.02741,
            0.03709, 0.02113, 0.03343, 0.02011, 0.03675, 0.03077,
            0.02201, 0.04844, 0.05518, 0.03765, 0.05433, 0.03049,
            0.04829, 0.02936, 0.04421, 0.02457, 0.04007, 0.03009,
            0.04504, 0.05041, 0.03651, 0.02719, 0.04383, 0.02887,
            0.03440, 0.03348, 0.02364, 0.03496, 0.02549, 0.03284,
            0.03523, 0.02579, 0.03080, 0.01784, 0.03237, 0.02078,
            0.03508, 0.03062, 0.02006, 0.02341, 0.02223, 0.03145,
            0.03081, 0.02520, 0.02683, 0.01720, 0.02225, 0.01579,
            0.02237, 0.02295, 0.01830, 0.02356, 0.02051, 0.02932,
            0.03025, 0.02390, 0.02635, 0.01863, 0.02994, 0.01762,
            0.02837, 0.02421, 0.01951, 0.02149, 0.02079, 0.02528,
            0.02575, 0.01634, 0.02563, 0.01719, 0.02915, 0.01724,
            0.02804, 0.02750, 0.02099, 0.02522, 0.02422, 0.03254,
            0.02095, 0.03241, 0.01867, 0.03998, 0.02212, 0.03034,
            0.03419, 0.01866, 0.02623, 0.02052]
      ue = [4.9, 5.0, 5.0, 5.0, 4.9, 4.7, 4.8, 4.7, 4.7,
            4.6, 4.6, 4.7, 4.7, 4.5, 4.4, 4.5, 4.4, 4.6,
            4.5, 4.4, 4.5, 4.4, 4.6, 4.7, 4.6, 4.7, 4.7,
            4.7, 5.0, 5.0, 4.9, 5.1, 5.0, 5.4, 5.6, 5.8,
            6.1, 6.1, 6.5, 6.8, 7.3, 7.8, 8.3, 8.7, 9.0,
            9.4, 9.5, 9.5, 9.6, 9.8, 10., 9.9, 9.9, 9.7,
            9.8, 9.9, 9.9, 9.6, 9.4, 9.5, 9.5, 9.5, 9.5,
            9.8, 9.4, 9.1, 9.0, 9.0, 9.1, 9.0, 9.1, 9.0,
            9.0, 9.0, 8.8, 8.6, 8.5, 8.2, 8.3, 8.2, 8.2,
            8.2, 8.2, 8.2, 8.1, 7.8, 7.8, 7.8, 7.9, 7.9,
            7.7, 7.5, 7.5, 7.5, 7.5, 7.3, 7.2, 7.2, 7.2,
            7.0, 6.7, 6.6, 6.7, 6.7, 6.3, 6.3]
  
      ue = np.array(ue) / 100
      model = ARIMA(ef, (1, 1, 1), exog=ue)
      res = model.fit(transparams=False, pgtol=1e-8, iprint=0, disp=0)
      assert_equal(res.mle_retvals['warnflag'], 0)
      predicts = res.predict(start=len(ef), end=len(ef) + 10,
                             exog=ue[-11:], typ='levels')
  
      # regression test, not verified numbers
      predicts_res = np.array([
          0.02591095, 0.02321325, 0.02436579, 0.02368759, 0.02389753,
          0.02372, 0.0237481, 0.0236738, 0.023644, 0.0236283,
          0.02362267])
  
      assert_allclose(predicts, predicts_res, atol=5e-6)
  
      # Smoke check of forecast with exog in ARIMA
      res.forecast(steps=10, exog=np.empty(10))
  
      with pytest.raises(ValueError):
          res.forecast(steps=10)
      with pytest.raises(ValueError):
          res.forecast(steps=10, exog=np.empty((10, 2)))
      with pytest.raises(ValueError):
          res.forecast(steps=10, exog=np.empty(100))
  
  
  def test_arima_exog_predict():
      # test forecasting and dynamic prediction with exog against Stata
  
      dta = load_macrodata_pandas().data
      dates = pd.date_range("1959", periods=len(dta), freq='Q')
      cpi_dates = period_range(start='1959Q1', end='2009Q3', freq='Q')
      dta.index = cpi_dates
  
      data = dta
      data['loginv'] = np.log(data['realinv'])
      data['loggdp'] = np.log(data['realgdp'])
      data['logcons'] = np.log(data['realcons'])
  
      forecast_period = period_range(start='2008Q2', end='2009Q4', freq='Q')
      end = forecast_period[0]
      data_sample = data.loc[dta.index < end]
  
      exog_full = data[['loggdp', 'logcons']]
  
      # pandas
  
      mod = ARIMA(data_sample['loginv'], (1, 0, 1),
                  exog=data_sample[['loggdp', 'logcons']])
      with warnings.catch_warnings():
          warnings.simplefilter("ignore")
          res = mod.fit(disp=0, solver='bfgs', maxiter=5000)
  
      predicted_arma_fp = res.predict(start=197, end=202,
                                      exog=exog_full.values[197:]).values
      predicted_arma_dp = res.predict(start=193, end=202,
                                      exog=exog_full[197:], dynamic=True)
  
      # numpy
      mod2 = ARIMA(np.asarray(data_sample['loginv']), (1, 0, 1),
                   exog=np.asarray(data_sample[['loggdp', 'logcons']]))
      res2 = mod2.fit(start_params=res.params, disp=0,
                      solver='bfgs', maxiter=5000)
  
      exog_full = data[['loggdp', 'logcons']]
      predicted_arma_f = res2.predict(start=197, end=202,
                                      exog=exog_full.values[197:])
      predicted_arma_d = res2.predict(start=193, end=202,
                                      exog=exog_full[197:], dynamic=True)
  
      endog_scale = 100
      ex_scale = 1000
      # ARIMA(1, 1, 1)
      ex = ex_scale * np.asarray(data_sample[['loggdp', 'logcons']].diff())
      # The first obsevation is not (supposed to be) used, but I get a Lapack problem
      # Intel MKL ERROR: Parameter 5 was incorrect on entry to DLASCL.
      ex[0] = 0
      mod111 = ARIMA(100 * np.asarray(data_sample['loginv']), (1, 1, 1),
                     # Stata differences also the exog
                     exog=ex)
      sv = [-0.94771574, 0.5869353, -0.32651653, 0.78066562, -0.68747501]
      res111 = mod111.fit(start_params=sv, disp=0, solver='bfgs', maxiter=5000)
      exog_full_d = ex_scale * data[['loggdp', 'logcons']].diff()
      res111.predict(start=197, end=202, exog=exog_full_d.values[197:])
  
      predicted_arima_f = res111.predict(start=196, end=202,
                                         exog=exog_full_d.values[197:],
                                         typ='levels')
      predicted_arima_d = res111.predict(start=193, end=202,
                                         exog=exog_full_d.values[197:],
                                         typ='levels', dynamic=True)
  
      res_f101 = np.array(
          [7.73975859954, 7.71660108543, 7.69808978329, 7.70872117504,
           7.65183927580, 7.69784279784, 7.70290907856, 7.69237782644,
           7.65017785174, 7.66061689028, 7.65980022857, 7.61505314129,
           7.51697158428, 7.51657606630, 7.5271053284])
      res_f111 = np.array(
          [7.74460013693, 7.71958207517, 7.69629561172, 7.71208186737,
           7.65758850178, 7.69223472572, 7.70411775588, 7.68896109499,
           7.64016249001, 7.64871881901, 7.62550283402, 7.55814609462,
           7.44431310053, 7.42963968062, 7.43554675427])
      res_d111 = np.array(
          [7.74460013693, 7.71958207517, 7.69629561172, 7.71208186737,
           7.65758850178, 7.69223472572, 7.71870821151, 7.72994302150,
           7.71439447355, 7.72544001101, 7.70521902623, 7.64020040524,
           7.52819271910, 7.51494426940, 7.52196378005])
      res_d101 = np.array(
          [7.73975859954, 7.71660108543, 7.69808978329, 7.70872117504,
           7.65183927580, 7.69784279784, 7.72522142662, 7.73962377858,
           7.73245950636, 7.74935432862, 7.74449584691, 7.69589103679,
           7.59412746880, 7.59021764836, 7.59739267775])
  
      # Relax tolerance on OSX due to frequent small failures
      # GH 4657
      tol = 1e-3 if PLATFORM_OSX or PLATFORM_WIN else 1e-4
      assert_allclose(predicted_arma_dp,
                      res_d101[-len(predicted_arma_d):], rtol=tol, atol=tol)
      assert_allclose(predicted_arma_fp,
                      res_f101[-len(predicted_arma_f):], rtol=tol, atol=tol)
      assert_allclose(predicted_arma_d,
                      res_d101[-len(predicted_arma_d):], rtol=tol, atol=tol)
      assert_allclose(predicted_arma_f,
                      res_f101[-len(predicted_arma_f):], rtol=tol, atol=tol)
      assert_allclose(predicted_arima_d / endog_scale,
                      res_d111[-len(predicted_arima_d):], rtol=tol, atol=tol)
      assert_allclose(predicted_arima_f / endog_scale,
                      res_f111[-len(predicted_arima_f):], rtol=tol, atol=tol)
  
      # test for forecast with 0 ar fix in #2457 numbers again from Stata
  
      res_f002 = np.array(
          [7.70178181209, 7.67445481224, 7.67153737650, 7.67729153190,
           7.61173201163, 7.67913499878, 7.67276092120, 7.66275451925,
           7.65199799315, 7.65149983741, 7.65554131408, 7.62213286298,
           7.53795983357, 7.53626130154, 7.54539963934])
      res_d002 = np.array(
          [7.70178181209, 7.67445481224, 7.67153737650, 7.67729153190,
           7.61173201163, 7.67913499878, 7.67306697759, 7.65287924998,
           7.64904451605, 7.66580449603, 7.66252081172, 7.62213286298,
           7.53795983357, 7.53626130154, 7.54539963934])
  
      mod_002 = ARIMA(np.asarray(data_sample['loginv']), (0, 0, 2),
                      exog=np.asarray(data_sample[['loggdp', 'logcons']]))
  
      # does not converge with default starting values
      start_params = np.concatenate((res.params[[0, 1, 2, 4]], [0]))
      res_002 = mod_002.fit(start_params=start_params, disp=0,
                            solver='bfgs', maxiter=5000)
  
      # forecast
      fpredict_002 = res_002.predict(start=197, end=202,
                                     exog=exog_full.values[197:])
      forecast_002 = res_002.forecast(steps=len(exog_full.values[197:]),
                                      exog=exog_full.values[197:])
      # TODO: Checking other results
      forecast_002 = forecast_002[0]
      assert_allclose(fpredict_002, res_f002[-len(fpredict_002):],
                      rtol=tol, atol=tol / 100.0)
      assert_allclose(forecast_002, res_f002[-len(forecast_002):],
                      rtol=tol, atol=tol / 100.0)
  
      # dynamic predict
      dpredict_002 = res_002.predict(start=193, end=202,
                                     exog=exog_full.values[197:], dynamic=True)
      assert_allclose(dpredict_002, res_d002[-len(dpredict_002):],
                      rtol=tol, atol=tol / 100.0)
  
      # in-sample dynamic predict should not need exog, #2982
      predict_3a = res_002.predict(start=100, end=120, dynamic=True)
      predict_3b = res_002.predict(start=100, end=120,
                                   exog=exog_full.values[100:120], dynamic=True)
      assert_allclose(predict_3a, predict_3b, rtol=1e-10)
  
      h = len(exog_full.values[197:])
      with pytest.raises(ValueError):
          res_002.forecast(steps=h)
      with pytest.raises(ValueError):
          res_002.forecast(steps=h, exog=np.empty((h, 20)))
      with pytest.raises(ValueError):
          res_002.forecast(steps=h, exog=np.empty(20))
  
  
  def test_arima_fit_multiple_calls():
      y = [-1214.360173, -1848.209905, -2100.918158, -3647.483678, -4711.186773]
      mod = ARIMA(y, (1, 0, 2))
      # Make multiple calls to fit
      with pytest.warns(HessianInversionWarning, match="no bse or cov"):
          mod.fit(disp=0, start_params=[np.mean(y), .1, .1, .1])
      assert_equal(mod.exog_names,  ['const', 'ar.L1.y', 'ma.L1.y', 'ma.L2.y'])
  
      mod.exog = None  # FIXME: this should not be necessary
      with pytest.warns(HessianInversionWarning, match="no bse or cov"):
          res = mod.fit(disp=0, start_params=[np.mean(y), .1, .1, .1])
      assert_equal(mod.exog_names,  ['const', 'ar.L1.y', 'ma.L1.y', 'ma.L2.y'])
  
      # ensure summary() works  # TODO: separate and pytest.mark.smoke
      res.summary()
  
      # test multiple calls when there is only a constant term
      mod = ARIMA(y, (0, 0, 0))
      # Make multiple calls to fit
      mod.fit(disp=0, start_params=[np.mean(y)])
      assert_equal(mod.exog_names,  ['const'])
  
      mod.exog = None  # FIXME: this should not be necessary
      res = mod.fit(disp=0, start_params=[np.mean(y)])
      assert_equal(mod.exog_names,  ['const'])
  
      # ensure summary() works  # TODO: separate and pytest.mark.smoke
      res.summary()
  
  
  def test_long_ar_start_params():
      np.random.seed(12345)
      arparams = np.array([1, -.75, .25])
      maparams = np.array([1, .65, .35])
  
      nobs = 30
  
      np.random.seed(12345)
      y = arma_generate_sample(arparams, maparams, nobs)
  
      model = ARMA(y, order=(2, 2))
  
      model.fit(method='css',start_ar_lags=10, disp=0)
  
      model.exog = None  # FIXME: should not be necessary
      model.fit(method='css-mle',start_ar_lags=10, disp=0)
  
      model.exog = None  # FIXME: should not be necessary
      model.fit(method='mle',start_ar_lags=10, disp=0)
      assert_raises(ValueError, model.fit, start_ar_lags=nobs+5, disp=0)
  
  
  def test_arma_pickle():
      np.random.seed(9876565)
      x = fa.ArmaFft([1, -0.5], [1., 0.4], 40).generate_sample(nsample=200,
                                                               burnin=1000)
      mod = ARMA(x, (1, 1))
      pkl_mod = pickle.loads(pickle.dumps(mod))
  
      res = mod.fit(trend="c", disp=-1, solver='newton')
      pkl_res = pkl_mod.fit(trend="c", disp=-1, solver='newton')
  
      assert_allclose(res.params, pkl_res.params)
      assert_allclose(res.llf, pkl_res.llf)
      assert_almost_equal(res.resid, pkl_res.resid)
      assert_almost_equal(res.fittedvalues, pkl_res.fittedvalues)
      assert_almost_equal(res.pvalues, pkl_res.pvalues)
  
  
  def test_arima_pickle():
      endog = y_arma[:, 6]
      mod = ARIMA(endog, (1, 1, 1))
      pkl_mod = pickle.loads(pickle.dumps(mod))
  
      res = mod.fit(trend="c", disp=-1, solver='newton')
      pkl_res = pkl_mod.fit(trend="c", disp=-1, solver='newton')
  
      assert_allclose(res.params, pkl_res.params)
      assert_allclose(res.llf, pkl_res.llf)
      assert_almost_equal(res.resid, pkl_res.resid)
      assert_almost_equal(res.fittedvalues, pkl_res.fittedvalues)
      assert_almost_equal(res.pvalues, pkl_res.pvalues)
  
  
  def test_arima_not_implemented():
      formula = ' WUE ~ 1 + SFO3 '
      data = [-1214.360173, -1848.209905, -2100.918158]
      assert_raises(NotImplementedError, ARIMA.from_formula, formula, data)
  
  
  def test_endog_int():
      # int endog should produce same result as float, #3504
  
      np.random.seed(123987)
      y = np.random.randint(0, 16, size=100)
      yf = y.astype(np.float64)
  
      res = AR(y).fit(5)
      resf = AR(yf).fit(5)
      assert_allclose(res.params, resf.params, atol=1e-5)
      assert_allclose(res.bse, resf.bse, atol=1e-5)
  
      res = ARMA(y, order=(2, 1)).fit(disp=0)
      resf = ARMA(yf, order=(2, 1)).fit(disp=0)
      assert_allclose(res.params, resf.params, atol=1e-5)
      assert_allclose(res.bse, resf.bse, atol=1e-5)
  
      res = ARIMA(y.cumsum(), order=(1, 1, 1)).fit(disp=0)
      resf = ARIMA(yf.cumsum(), order=(1, 1, 1)).fit(disp=0)
      assert_allclose(res.params, resf.params, rtol=1e-6, atol=1e-5)
      assert_allclose(res.bse, resf.bse, rtol=1e-6, atol=1e-5)
  
  
  def test_multidim_endog(reset_randomstate):
      y = np.random.randn(1000, 2)
      with pytest.raises(ValueError):
          ARMA(y, order=(1, 1))
  
      y = np.random.randn(1000, 1, 2)
      with pytest.raises(ValueError):
          ARMA(y, order=(1, 1))
  
      y = np.random.randn(1, 1, 1000)
      with pytest.raises(ValueError):
          ARMA(y, order=(1, 1))
  
  
  def test_arima_no_full_output():
      # GH 2752
      endog = y_arma[:, 6]
      mod = ARIMA(endog, (1, 0, 1))
      res = mod.fit(trend="c", disp=-1, full_output=False)
      assert res.mle_retvals is None
  
  
  def test_arima_summary_no_lags(reset_randomstate):
      y_train = pd.Series(np.random.randn(1000), name='y_train')
      x_train = pd.DataFrame(np.random.randn(1000, 2), columns=['x1', 'x2'])
      res = ARIMA(endog=y_train.values, exog=x_train,
                  order=(0, 1, 0)).fit(disp=-1)
      summ = res.summary().as_text()
      assert 'const ' in summ
      assert 'x1 ' in summ
      assert 'x2 ' in summ
  
  
  def test_constant_column_trend():
      # GH#3343 analogous to GH#5258 for AR, when the user passes a constant exog
      #  and also passes trend="c", raise instead _make_arma_exog used to
      #  silently drop a column and return an inconsistenct k_trend value.
  
      exog = np.array([0.5, 0.5, 0.5, 0.5, 0.5])
      endog =  np.array([-0.011866, 0.003380, 0.015357, 0.004451, -0.020889])
  
      model = ARIMA(endog=endog, order=(1, 1, 0), exog=exog)
  
      # Fitting with a constant and constant exog raises because of colinearity
      with pytest.raises(ValueError, match="x contains a constant"):
          model.fit(trend="c")
  
      # FIXME: calling model.fit(trend="nc") raises for orthogonal reasons
  
apis: numpy.ones pandas.Series numpy.diff numpy.random.seed numpy.asarray numpy.ones_like numpy.log pandas.period_range numpy.testing.assert_almost_equal numpy.genfromtxt numpy.mean pandas.date_range numpy.zeros pandas.read_csv pandas.Index numpy.testing.assert_raises pandas.DatetimeIndex numpy.cumsum numpy.empty pandas.DataFrame numpy.random.randn numpy.random.random numpy.testing.assert_allclose numpy.array numpy.concatenate numpy.random.randint