code: def test_predicted_filtered_smoothed_with_nans_TVSS(
      reset_randomstate,
  ):
      mod = TVSS(np.zeros((50, 2)) * np.nan)
      mod.ssm.initialize_known([1.2, 0.8], np.eye(2))
      res = mod.smooth([])
  
      mod_oos = TVSS(np.zeros((11, 2)) * np.nan)
      kwargs = {
          key: mod_oos[key]
          for key in [
              "obs_intercept",
              "design",
              "obs_cov",
              "transition",
              "selection",
              "state_cov",
          ]
      }
  
      p_pred = res.get_prediction(
          start=0, end=60, information_set="predicted", **kwargs
      )
  
      f_pred = res.get_prediction(
          start=0, end=60, information_set="filtered", **kwargs
      )
  
      s_pred = res.get_prediction(
          start=0, end=60, information_set="smoothed", **kwargs
      )
  
      # Test forecasts
      assert_allclose(s_pred.predicted_mean, p_pred.predicted_mean)
      assert_allclose(s_pred.var_pred_mean, p_pred.var_pred_mean)
      assert_allclose(f_pred.predicted_mean, p_pred.predicted_mean)
      assert_allclose(f_pred.var_pred_mean, p_pred.var_pred_mean)
      assert_allclose(p_pred.predicted_mean[:50], res.fittedvalues)
      assert_allclose(
          p_pred.var_pred_mean[:50].T, res.forecasts_error_cov
      )
  
      p_signal = res.get_prediction(
          start=0,
          end=60,
          information_set="predicted",
          signal_only=True,
          **kwargs,
      )
  
      f_signal = res.get_prediction(
          start=0,
          end=60,
          information_set="filtered",
          signal_only=True,
          **kwargs,
      )
  
      s_signal = res.get_prediction(
          start=0,
          end=60,
          information_set="smoothed",
          signal_only=True,
          **kwargs,
      )
  
      # Test signal predictions
      assert_allclose(s_signal.predicted_mean, p_signal.predicted_mean)
      assert_allclose(s_signal.var_pred_mean, p_signal.var_pred_mean)
      assert_allclose(f_signal.predicted_mean, p_signal.predicted_mean)
      assert_allclose(f_signal.var_pred_mean, p_signal.var_pred_mean)
      assert_allclose(
          p_signal.predicted_mean[:50] + mod["obs_intercept"].T,
          res.fittedvalues,
      )
      assert_allclose(
          (p_signal.var_pred_mean[:50] + mod["obs_cov"].T).T,
          res.forecasts_error_cov,
      )
  
file_path: statsmodels/statsmodels/tsa/statespace/tests/test_prediction.py
imports: import pytest
  import numpy
  import pandas
  from numpy.testing import assert_equal, assert_raises, assert_allclose, assert_
  from statsmodels import datasets
  from statsmodels.tsa.statespace import sarimax, varmax
  from statsmodels.tsa.statespace.tests.test_impulse_responses import TVSS
label_desc: Use image node_id 6 for calling a global function with example usage: test_predicted_filtered_smoothed_with_nans_TVSS(reset_randomstate) without return types