text: from scipy.stats import norm
  from numpy import array, polyval, inf, asarray
  
  __all__ = ['mackinnonp', 'mackinnoncrit']
  
  # These are the cut-off values for the left-tail vs. the rest of the
  # tau distribution, for getting the p-values
  
  tau_star_nc = [-1.04, -1.53, -2.68, -3.09, -3.07, -3.77]
  tau_min_nc = [-19.04, -19.62, -21.21, -23.25, -21.63, -25.74]
  tau_max_nc = [inf, 1.51, 0.86, 0.88, 1.05, 1.24]
  tau_star_c = [-1.61, -2.62, -3.13, -3.47, -3.78, -3.93]
  tau_min_c = [-18.83, -18.86, -23.48, -28.07, -25.96, -23.27]
  tau_max_c = [2.74, 0.92, 0.55, 0.61, 0.79, 1]
  tau_star_ct = [-2.89, -3.19, -3.50, -3.65, -3.80, -4.36]
  tau_min_ct = [-16.18, -21.15, -25.37, -26.63, -26.53, -26.18]
  tau_max_ct = [0.7, 0.63, 0.71, 0.93, 1.19, 1.42]
  tau_star_ctt = [-3.21, -3.51, -3.81, -3.83, -4.12, -4.63]
  tau_min_ctt = [-17.17, -21.1, -24.33, -24.03, -24.33, -28.22]
  tau_max_ctt = [0.54, 0.79, 1.08, 1.43, 3.49, 1.92]
  
  _tau_maxs = {
      "nc": tau_max_nc,
      "c": tau_max_c,
      "ct": tau_max_ct,
      "ctt": tau_max_ctt,
  }
  _tau_mins = {
      "nc": tau_min_nc,
      "c": tau_min_c,
      "ct": tau_min_ct,
      "ctt": tau_min_ctt,
  }
  _tau_stars = {
      "nc": tau_star_nc,
      "c": tau_star_c,
      "ct": tau_star_ct,
      "ctt": tau_star_ctt,
  }
  
  
  small_scaling = array([1, 1, 1e-2])
  tau_nc_smallp = [
      [0.6344, 1.2378, 3.2496],
      [1.9129, 1.3857, 3.5322],
      [2.7648, 1.4502, 3.4186],
      [3.4336, 1.4835, 3.19],
      [4.0999, 1.5533, 3.59],
      [4.5388, 1.5344, 2.9807]]
  tau_nc_smallp = asarray(tau_nc_smallp)*small_scaling
  
  tau_c_smallp = [
      [2.1659, 1.4412, 3.8269],
      [2.92, 1.5012, 3.9796],
      [3.4699, 1.4856, 3.164],
      [3.9673, 1.4777, 2.6315],
      [4.5509, 1.5338, 2.9545],
      [5.1399, 1.6036, 3.4445]]
  tau_c_smallp = asarray(tau_c_smallp)*small_scaling
  
  tau_ct_smallp = [
      [3.2512, 1.6047, 4.9588],
      [3.6646, 1.5419, 3.6448],
      [4.0983, 1.5173, 2.9898],
      [4.5844, 1.5338, 2.8796],
      [5.0722, 1.5634, 2.9472],
      [5.53, 1.5914, 3.0392]]
  tau_ct_smallp = asarray(tau_ct_smallp)*small_scaling
  
  tau_ctt_smallp = [
      [4.0003, 1.658, 4.8288],
      [4.3534, 1.6016, 3.7947],
      [4.7343, 1.5768, 3.2396],
      [5.214, 1.6077, 3.3449],
      [5.6481, 1.6274, 3.3455],
      [5.9296, 1.5929, 2.8223]]
  tau_ctt_smallp = asarray(tau_ctt_smallp)*small_scaling
  
  _tau_smallps = {
      "nc": tau_nc_smallp,
      "c": tau_c_smallp,
      "ct": tau_ct_smallp,
      "ctt": tau_ctt_smallp,
  }
  
  
  large_scaling = array([1, 1e-1, 1e-1, 1e-2])
  tau_nc_largep = [
      [0.4797, 9.3557, -0.6999, 3.3066],
      [1.5578, 8.558, -2.083, -3.3549],
      [2.2268, 6.8093, -3.2362, -5.4448],
      [2.7654, 6.4502, -3.0811, -4.4946],
      [3.2684, 6.8051, -2.6778, -3.4972],
      [3.7268, 7.167, -2.3648, -2.8288]]
  tau_nc_largep = asarray(tau_nc_largep)*large_scaling
  
  tau_c_largep = [
      [1.7339, 9.3202, -1.2745, -1.0368],
      [2.1945, 6.4695, -2.9198, -4.2377],
      [2.5893, 4.5168, -3.6529, -5.0074],
      [3.0387, 4.5452, -3.3666, -4.1921],
      [3.5049, 5.2098, -2.9158, -3.3468],
      [3.9489, 5.8933, -2.5359, -2.721]]
  tau_c_largep = asarray(tau_c_largep)*large_scaling
  
  tau_ct_largep = [
      [2.5261, 6.1654, -3.7956, -6.0285],
      [2.85, 5.272, -3.6622, -5.1695],
      [3.221, 5.255, -3.2685, -4.1501],
      [3.652, 5.9758, -2.7483, -3.2081],
      [4.0712, 6.6428, -2.3464, -2.546],
      [4.4735, 7.1757, -2.0681, -2.1196]]
  tau_ct_largep = asarray(tau_ct_largep)*large_scaling
  
  tau_ctt_largep = [
      [3.0778, 4.9529, -4.1477, -5.9359],
      [3.4713, 5.967, -3.2507, -4.2286],
      [3.8637, 6.7852, -2.6286, -3.1381],
      [4.2736, 7.6199, -2.1534, -2.4026],
      [4.6679, 8.2618, -1.822, -1.9147],
      [5.0009, 8.3735, -1.6994, -1.6928]]
  tau_ctt_largep = asarray(tau_ctt_largep)*large_scaling
  
  _tau_largeps = {
      "nc": tau_nc_largep,
      "c": tau_c_largep,
      "ct": tau_ct_largep,
      "ctt": tau_ctt_largep,
  }
  
  
  # NOTE: The Z-statistic is used when lags are included to account for
  #  serial correlation in the error term
  
  z_star_nc = [-2.9, -8.7, -14.8, -20.9, -25.7, -30.5]
  z_star_c = [-8.9, -14.3, -19.5, -25.1, -29.6, -34.4]
  z_star_ct = [-15.0, -19.6, -25.3, -29.6, -31.8, -38.4]
  z_star_ctt = [-20.7, -25.3, -29.9, -34.4, -38.5, -44.2]
  
  
  # These are Table 5 from MacKinnon (1994)
  # small p is defined as p in .005 to .150 ie p = .005 up to z_star
  # Z* is the largest value for which it is appropriate to use these
  # approximations
  # the left tail approximation is
  # p = norm.cdf(d_0 + d_1*log(abs(z)) + d_2*log(abs(z))**2 + d_3*log(abs(z))**3)
  # there is no Z-min, ie., it is well-behaved in the left tail
  
  z_nc_smallp = array([
      [.0342, -.6376, 0, -.03872],
      [1.3426, -.7680, 0, -.04104],
      [3.8607, -2.4159, .51293, -.09835],
      [6.1072, -3.7250, .85887, -.13102],
      [7.7800, -4.4579, 1.00056, -.14014],
      [4.0253, -.8815, 0, -.04887]])
  
  z_c_smallp = array([
      [2.2142, -1.7863, .32828, -.07727],
      [1.1662, .1814, -.36707, 0],
      [6.6584, -4.3486, 1.04705, -.15011],
      [3.3249, -.8456, 0, -.04818],
      [4.0356, -.9306, 0, -.04776],
      [13.9959, -8.4314, 1.97411, -.22234]])
  
  z_ct_smallp = array([
      [4.6476, -2.8932, 0.5832, -0.0999],
      [7.2453, -4.7021, 1.127, -.15665],
      [3.4893, -0.8914, 0, -.04755],
      [1.6604, 1.0375, -0.53377, 0],
      [2.006, 1.1197, -0.55315, 0],
      [11.1626, -5.6858, 1.21479, -.15428]])
  
  z_ctt_smallp = array([
      [3.6739, -1.1549, 0, -0.03947],
      [3.9783, -1.0619, 0, -0.04394],
      [2.0062, 0.8907, -0.51708, 0],
      [4.9218, -1.0663, 0, -0.04691],
      [5.1433, -0.9877, 0, -0.04993],
      [23.6812, -14.6485, 3.42909, -.33794]])
  # These are Table 6 from MacKinnon (1994).
  # These are well-behaved in the right tail.
  # the approximation function is
  # p = norm.cdf(d_0 + d_1 * z + d_2*z**2 + d_3*z**3 + d_4*z**4)
  z_large_scaling = array([1, 1e-1, 1e-2, 1e-3, 1e-5])
  z_nc_largep = array([
      [0.4927, 6.906, 13.2331, 12.099, 0],
      [1.5167, 4.6859, 4.2401, 2.7939, 7.9601],
      [2.2347, 3.9465, 2.2406, 0.8746, 1.4239],
      [2.8239, 3.6265, 1.6738, 0.5408, 0.7449],
      [3.3174, 3.3492, 1.2792, 0.3416, 0.3894],
      [3.729, 3.0611, 0.9579, 0.2087, 0.1943]])
  z_nc_largep *= z_large_scaling
  
  z_c_largep = array([
      [1.717, 5.5243, 4.3463, 1.6671, 0],
      [2.2394, 4.2377, 2.432, 0.9241, 0.4364],
      [2.743, 3.626, 1.5703, 0.4612, 0.567],
      [3.228, 3.3399, 1.2319, 0.3162, 0.3482],
      [3.6583, 3.0934, 0.9681, 0.2111, 0.1979],
      [4.0379, 2.8735, 0.7694, 0.1433, 0.1146]])
  z_c_largep *= z_large_scaling
  
  z_ct_largep = array([
      [2.7117, 4.5731, 2.2868, 0.6362, 0.5],
      [3.0972, 4.0873, 1.8982, 0.5796, 0.7384],
      [3.4594, 3.6326, 1.4284, 0.3813, 0.4325],
      [3.806, 3.2634, 1.0689, 0.2402, 0.2304],
      [4.1402, 2.9867, 0.8323, 0.16, 0.1315],
      [4.4497, 2.7534, 0.6582, 0.1089, 0.0773]])
  z_ct_largep *= z_large_scaling
  
  z_ctt_largep = array([
      [3.4671, 4.3476, 1.9231, 0.5381, 0.6216],
      [3.7827, 3.9421, 1.5699, 0.4093, 0.4485],
      [4.052, 3.4947, 1.1772, 0.2642, 0.2502],
      [4.3311, 3.1625, 0.9126, 0.1775, 0.1462],
      [4.594, 2.8739, 0.707, 0.1181, 0.0838],
      [4.8479, 2.6447, 0.5647, 0.0827, 0.0518]])
  z_ctt_largep *= z_large_scaling
  
  
  # TODO: finish this and then integrate them into adf function
  def mackinnonp(teststat, regression="c", N=1, lags=None):
      """
      Returns MacKinnon's approximate p-value for teststat.
  
      Parameters
      ----------
      teststat : float
          "T-value" from an Augmented Dickey-Fuller regression.
      regression : str {"c", "nc", "ct", "ctt"}
          This is the method of regression that was used.  Following MacKinnon's
          notation, this can be "c" for constant, "nc" for no constant, "ct" for
          constant and trend, and "ctt" for constant, trend, and trend-squared.
      N : int
          The number of series believed to be I(1).  For (Augmented) Dickey-
          Fuller N = 1.
  
      Returns
      -------
      p-value : float
          The p-value for the ADF statistic estimated using MacKinnon 1994.
  
      References
      ----------
      MacKinnon, J.G. 1994  "Approximate Asymptotic Distribution Functions for
          Unit-Root and Cointegration Tests." Journal of Business & Economics
          Statistics, 12.2, 167-76.
  
      Notes
      -----
      For (A)DF
      H_0: AR coefficient = 1
      H_a: AR coefficient < 1
      """
      maxstat = _tau_maxs[regression]
      minstat = _tau_mins[regression]
      starstat = _tau_stars[regression]
      if teststat > maxstat[N-1]:
          return 1.0
      elif teststat < minstat[N-1]:
          return 0.0
      if teststat <= starstat[N-1]:
          tau_coef = _tau_smallps[regression][N-1]
      else:
          # Note: above is only for z stats
          tau_coef = _tau_largeps[regression][N-1]
      return norm.cdf(polyval(tau_coef[::-1], teststat))
  
  
  # These are the new estimates from MacKinnon 2010
  # the first axis is N -1
  # the second axis is 1 %, 5 %, 10 %
  # the last axis is the coefficients
  
  tau_nc_2010 = [[
      [-2.56574, -2.2358, -3.627, 0],  # N = 1
      [-1.94100, -0.2686, -3.365, 31.223],
      [-1.61682, 0.2656, -2.714, 25.364]]]
  tau_nc_2010 = asarray(tau_nc_2010)
  
  tau_c_2010 = [
      [[-3.43035, -6.5393, -16.786, -79.433],  # N = 1, 1%
       [-2.86154, -2.8903, -4.234, -40.040],   # 5 %
       [-2.56677, -1.5384, -2.809, 0]],        # 10 %
      [[-3.89644, -10.9519, -33.527, 0],       # N = 2
       [-3.33613, -6.1101, -6.823, 0],
       [-3.04445, -4.2412, -2.720, 0]],
      [[-4.29374, -14.4354, -33.195, 47.433],  # N = 3
       [-3.74066, -8.5632, -10.852, 27.982],
       [-3.45218, -6.2143, -3.718, 0]],
      [[-4.64332, -18.1031, -37.972, 0],       # N = 4
       [-4.09600, -11.2349, -11.175, 0],
       [-3.81020, -8.3931, -4.137, 0]],
      [[-4.95756, -21.8883, -45.142, 0],       # N = 5
       [-4.41519, -14.0405, -12.575, 0],
       [-4.13157, -10.7417, -3.784, 0]],
      [[-5.24568, -25.6688, -57.737, 88.639],  # N = 6
       [-4.70693, -16.9178, -17.492, 60.007],
       [-4.42501, -13.1875, -5.104, 27.877]],
      [[-5.51233, -29.5760, -69.398, 164.295],  # N = 7
       [-4.97684, -19.9021, -22.045, 110.761],
       [-4.69648, -15.7315, -5.104, 27.877]],
      [[-5.76202, -33.5258, -82.189, 256.289],  # N = 8
       [-5.22924, -23.0023, -24.646, 144.479],
       [-4.95007, -18.3959, -7.344, 94.872]],
      [[-5.99742, -37.6572, -87.365, 248.316],  # N = 9
       [-5.46697, -26.2057, -26.627, 176.382],
       [-5.18897, -21.1377, -9.484, 172.704]],
      [[-6.22103, -41.7154, -102.680, 389.33],  # N = 10
       [-5.69244, -29.4521, -30.994, 251.016],
       [-5.41533, -24.0006, -7.514, 163.049]],
      [[-6.43377, -46.0084, -106.809, 352.752],  # N = 11
       [-5.90714, -32.8336, -30.275, 249.994],
       [-5.63086, -26.9693, -4.083, 151.427]],
      [[-6.63790, -50.2095, -124.156, 579.622],  # N = 12
       [-6.11279, -36.2681, -32.505, 314.802],
       [-5.83724, -29.9864, -2.686, 184.116]]]
  tau_c_2010 = asarray(tau_c_2010)
  
  tau_ct_2010 = [
      [[-3.95877, -9.0531, -28.428, -134.155],   # N = 1
       [-3.41049, -4.3904, -9.036, -45.374],
       [-3.12705, -2.5856, -3.925, -22.380]],
      [[-4.32762, -15.4387, -35.679, 0],         # N = 2
       [-3.78057, -9.5106, -12.074, 0],
       [-3.49631, -7.0815, -7.538, 21.892]],
      [[-4.66305, -18.7688, -49.793, 104.244],   # N = 3
       [-4.11890, -11.8922, -19.031, 77.332],
       [-3.83511, -9.0723, -8.504, 35.403]],
      [[-4.96940, -22.4694, -52.599, 51.314],    # N = 4
       [-4.42871, -14.5876, -18.228, 39.647],
       [-4.14633, -11.2500, -9.873, 54.109]],
      [[-5.25276, -26.2183, -59.631, 50.646],    # N = 5
       [-4.71537, -17.3569, -22.660, 91.359],
       [-4.43422, -13.6078, -10.238, 76.781]],
      [[-5.51727, -29.9760, -75.222, 202.253],   # N = 6
       [-4.98228, -20.3050, -25.224, 132.03],
       [-4.70233, -16.1253, -9.836, 94.272]],
      [[-5.76537, -33.9165, -84.312, 245.394],   # N = 7
       [-5.23299, -23.3328, -28.955, 182.342],
       [-4.95405, -18.7352, -10.168, 120.575]],
      [[-6.00003, -37.8892, -96.428, 335.92],    # N = 8
       [-5.46971, -26.4771, -31.034, 220.165],
       [-5.19183, -21.4328, -10.726, 157.955]],
      [[-6.22288, -41.9496, -109.881, 466.068],  # N = 9
       [-5.69447, -29.7152, -33.784, 273.002],
       [-5.41738, -24.2882, -8.584, 169.891]],
      [[-6.43551, -46.1151, -120.814, 566.823],  # N = 10
       [-5.90887, -33.0251, -37.208, 346.189],
       [-5.63255, -27.2042, -6.792, 177.666]],
      [[-6.63894, -50.4287, -128.997, 642.781],  # N = 11
       [-6.11404, -36.4610, -36.246, 348.554],
       [-5.83850, -30.1995, -5.163, 210.338]],
      [[-6.83488, -54.7119, -139.800, 736.376],  # N = 12
       [-6.31127, -39.9676, -37.021, 406.051],
       [-6.03650, -33.2381, -6.606, 317.776]]]
  tau_ct_2010 = asarray(tau_ct_2010)
  
  tau_ctt_2010 = [
      [[-4.37113, -11.5882, -35.819, -334.047],  # N = 1
       [-3.83239, -5.9057, -12.490, -118.284],
       [-3.55326, -3.6596, -5.293, -63.559]],
      [[-4.69276, -20.2284, -64.919, 88.884],    # N =2
       [-4.15387, -13.3114, -28.402, 72.741],
       [-3.87346, -10.4637, -17.408, 66.313]],
      [[-4.99071, -23.5873, -76.924, 184.782],   # N = 3
       [-4.45311, -15.7732, -32.316, 122.705],
       [-4.17280, -12.4909, -17.912, 83.285]],
      [[-5.26780, -27.2836, -78.971, 137.871],   # N = 4
       [-4.73244, -18.4833, -31.875, 111.817],
       [-4.45268, -14.7199, -17.969, 101.92]],
      [[-5.52826, -30.9051, -92.490, 248.096],   # N = 5
       [-4.99491, -21.2360, -37.685, 194.208],
       [-4.71587, -17.0820, -18.631, 136.672]],
      [[-5.77379, -34.7010, -105.937, 393.991],  # N = 6
       [-5.24217, -24.2177, -39.153, 232.528],
       [-4.96397, -19.6064, -18.858, 174.919]],
      [[-6.00609, -38.7383, -108.605, 365.208],  # N = 7
       [-5.47664, -27.3005, -39.498, 246.918],
       [-5.19921, -22.2617, -17.910, 208.494]],
      [[-6.22758, -42.7154, -119.622, 421.395],  # N = 8
       [-5.69983, -30.4365, -44.300, 345.48],
       [-5.42320, -24.9686, -19.688, 274.462]],
      [[-6.43933, -46.7581, -136.691, 651.38],   # N = 9
       [-5.91298, -33.7584, -42.686, 346.629],
       [-5.63704, -27.8965, -13.880, 236.975]],
      [[-6.64235, -50.9783, -145.462, 752.228],  # N = 10
       [-6.11753, -37.056, -48.719, 473.905],
       [-5.84215, -30.8119, -14.938, 316.006]],
      [[-6.83743, -55.2861, -152.651, 792.577],  # N = 11
       [-6.31396, -40.5507, -46.771, 487.185],
       [-6.03921, -33.8950, -9.122, 285.164]],
      [[-7.02582, -59.6037, -166.368, 989.879],  # N = 12
       [-6.50353, -44.0797, -47.242, 543.889],
       [-6.22941, -36.9673, -10.868, 418.414]]]
  tau_ctt_2010 = asarray(tau_ctt_2010)
  
  tau_2010s = {
      "nc": tau_nc_2010,
      "c": tau_c_2010,
      "ct": tau_ct_2010,
      "ctt": tau_ctt_2010,
  }
  
  
  def mackinnoncrit(N=1, regression="c", nobs=inf):
      """
      Returns the critical values for cointegrating and the ADF test.
  
      In 2010 MacKinnon updated the values of his 1994 paper with critical values
      for the augmented Dickey-Fuller tests.  These new values are to be
      preferred and are used here.
  
      Parameters
      ----------
      N : int
          The number of series of I(1) series for which the null of
          non-cointegration is being tested.  For N > 12, the critical values
          are linearly interpolated (not yet implemented).  For the ADF test,
          N = 1.
      reg : str {'c', 'tc', 'ctt', 'nc'}
          Following MacKinnon (1996), these stand for the type of regression run.
          'c' for constant and no trend, 'tc' for constant with a linear trend,
          'ctt' for constant with a linear and quadratic trend, and 'nc' for
          no constant.  The values for the no constant case are taken from the
          1996 paper, as they were not updated for 2010 due to the unrealistic
          assumptions that would underlie such a case.
      nobs : int or np.inf
          This is the sample size.  If the sample size is numpy.inf, then the
          asymptotic critical values are returned.
  
      References
      ----------
      MacKinnon, J.G. 1994  "Approximate Asymptotic Distribution Functions for
          Unit-Root and Cointegration Tests." Journal of Business & Economics
          Statistics, 12.2, 167-76.
      MacKinnon, J.G. 2010.  "Critical Values for Cointegration Tests."
          Queen's University, Dept of Economics Working Papers 1227.
          http://ideas.repec.org/p/qed/wpaper/1227.html
      """
      reg = regression
      if reg not in ['c', 'ct', 'nc', 'ctt']:
          raise ValueError("regression keyword %s not understood" % reg)
      tau = tau_2010s[reg]
      if nobs is inf:
          return tau[N-1, :, 0]
      else:
          val = tau[N-1, :, ::-1]
          return polyval(val.T, 1./nobs)
  