r"""
Tests for smoothing and estimation of unobserved states and disturbances

- Predicted states: :math:`E(\alpha_t | Y_{t-1})`
- Filtered states: :math:`E(\alpha_t | Y_t)`
- Smoothed states: :math:`E(\alpha_t | Y_n)`
- Smoothed disturbances :math:`E(\varepsilon_t | Y_n), E(\eta_t | Y_n)`

Tested against R (FKF, KalmanRun / KalmanSmooth), Stata (sspace), and
MATLAB (ssm toolbox)

Author: Chad Fulton
License: Simplified-BSD
"""
import os

import numpy as np
from numpy.testing import assert_allclose, assert_almost_equal, assert_equal
import pandas as pd
import pytest

from statsmodels import datasets
from statsmodels.tsa.statespace import mlemodel, sarimax, varmax
from statsmodels.tsa.statespace.kalman_filter import FILTER_UNIVARIATE
from statsmodels.tsa.statespace.kalman_smoother import (
    SMOOTH_ALTERNATIVE,
    SMOOTH_CLASSICAL,
    SMOOTH_UNIVARIATE,
)
from statsmodels.tsa.statespace.tests.test_impulse_responses import TVSS

current_path = os.path.dirname(os.path.abspath(__file__))


class TestStatesAR3:
    @classmethod
    def setup_class(cls, *args, alternate_timing=False, **kwargs):
        # Dataset / Stata comparison
        path = os.path.join(current_path, "results",
                            "results_wpi1_ar3_stata.csv")
        cls.stata = pd.read_csv(path)
        cls.stata.index = pd.date_range(start="1960-01-01", periods=124,
                                        freq="QS")
        # Matlab comparison
        path = os.path.join(current_path, "results",
                            "results_wpi1_ar3_matlab_ssm.csv")
        matlab_names = [
            "a1", "a2", "a3", "detP", "alphahat1", "alphahat2", "alphahat3",
            "detV", "eps", "epsvar", "eta", "etavar"
        ]
        cls.matlab_ssm = pd.read_csv(path, header=None, names=matlab_names)

        cls.model = sarimax.SARIMAX(
            cls.stata["wpi"],
            *args,
            order=(3, 1, 0),
            simple_differencing=True,
            hamilton_representation=True,
            **kwargs
        )

        if alternate_timing:
            cls.model.ssm.timing_init_filtered = True

        # Parameters from from Stata's sspace MLE estimation
        params = np.r_[.5270715, .0952613, .2580355, .5307459]
        cls.results = cls.model.smooth(params, cov_type="none")

        # Calculate the determinant of the covariance matrices (for easy
        # comparison to other languages without having to store 2-dim arrays)
        cls.results.det_predicted_state_cov = np.zeros((1, cls.model.nobs))
        cls.results.det_smoothed_state_cov = np.zeros((1, cls.model.nobs))
        for i in range(cls.model.nobs):
            cls.results.det_predicted_state_cov[0, i] = np.linalg.det(
                cls.results.filter_results.predicted_state_cov[:, :, i])
            cls.results.det_smoothed_state_cov[0, i] = np.linalg.det(
                cls.results.smoother_results.smoothed_state_cov[:, :, i])

        # Perform simulation smoothing
        nobs = cls.model.nobs
        k_endog = cls.model.k_endog
        k_posdef = cls.model.ssm.k_posdef
        cls.sim = cls.model.simulation_smoother(filter_timing=0)
        cls.sim.simulate(
            measurement_disturbance_variates=np.zeros(nobs * k_endog),
            state_disturbance_variates=np.zeros(nobs * k_posdef),
            initial_state_variates=np.zeros(cls.model.k_states)
        )

    def test_predict_obs(self):
        assert_almost_equal(
            self.results.filter_results.predict().forecasts[0],
            self.stata.iloc[1:]["dep1"], 4
        )

    def test_standardized_residuals(self):
        assert_almost_equal(
            self.results.filter_results.standardized_forecasts_error[0],
            self.stata.iloc[1:]["sr1"], 4
        )

    def test_predicted_states(self):
        assert_almost_equal(
            self.results.filter_results.predicted_state[:, :-1].T,
            self.stata.iloc[1:][["sp1", "sp2", "sp3"]], 4
        )
        assert_almost_equal(
            self.results.filter_results.predicted_state[:, :-1].T,
            self.matlab_ssm[["a1", "a2", "a3"]], 4
        )

    def test_predicted_states_cov(self):
        assert_almost_equal(
            self.results.det_predicted_state_cov.T,
            self.matlab_ssm[["detP"]], 4
        )

    def test_filtered_states(self):
        assert_almost_equal(
            self.results.filter_results.filtered_state.T,
            self.stata.iloc[1:][["sf1", "sf2", "sf3"]], 4
        )

    def test_smoothed_states(self):
        assert_almost_equal(
            self.results.smoother_results.smoothed_state.T,
            self.stata.iloc[1:][["sm1", "sm2", "sm3"]], 4
        )
        assert_almost_equal(
            self.results.smoother_results.smoothed_state.T,
            self.matlab_ssm[["alphahat1", "alphahat2", "alphahat3"]], 4
        )

    def test_smoothed_states_cov(self):
        assert_almost_equal(
            self.results.det_smoothed_state_cov.T,
            self.matlab_ssm[["detV"]], 4
        )

    def test_smoothed_measurement_disturbance(self):
        assert_almost_equal(
            self.results.smoother_results.smoothed_measurement_disturbance.T,
            self.matlab_ssm[["eps"]], 4
        )

    def test_smoothed_measurement_disturbance_cov(self):
        res = self.results.smoother_results
        assert_almost_equal(
            res.smoothed_measurement_disturbance_cov[0].T,
            self.matlab_ssm[["epsvar"]], 4
        )

    def test_smoothed_state_disturbance(self):
        assert_almost_equal(
            self.results.smoother_results.smoothed_state_disturbance.T,
            self.matlab_ssm[["eta"]], 4
        )

    def test_smoothed_state_disturbance_cov(self):
        assert_almost_equal(
            self.results.smoother_results.smoothed_state_disturbance_cov[0].T,
            self.matlab_ssm[["etavar"]], 4
        )


class TestStatesAR3AlternateTiming(TestStatesAR3):
    @classmethod
    def setup_class(cls, *args, **kwargs):
        super().setup_class(*args, alternate_timing=True, **kwargs)


class TestStatesAR3AlternativeSmoothing(TestStatesAR3):
    @classmethod
    def setup_class(cls, *args, **kwargs):
        super().setup_class(*args, smooth_method=SMOOTH_ALTERNATIVE, **kwargs)

    def test_smoothed_states(self):
        # Initialization issues can change the first few smoothed states
        assert_almost_equal(
            self.results.smoother_results.smoothed_state.T[2:],
            self.stata.iloc[3:][["sm1", "sm2", "sm3"]], 4
        )
        assert_almost_equal(
            self.results.smoother_results.smoothed_state.T[2:],
            self.matlab_ssm.iloc[2:][["alphahat1", "alphahat2", "alphahat3"]],
            4
        )

    def test_smoothed_states_cov(self):
        assert_almost_equal(
            self.results.det_smoothed_state_cov.T[1:],
            self.matlab_ssm.iloc[1:][["detV"]], 4
        )

    def test_smooth_method(self):
        assert_equal(self.model.ssm.smooth_method, SMOOTH_ALTERNATIVE)
        assert_equal(self.model.ssm._kalman_smoother.smooth_method,
                     SMOOTH_ALTERNATIVE)
        assert_equal(self.model.ssm._kalman_smoother._smooth_method,
                     SMOOTH_ALTERNATIVE)


class TestStatesAR3UnivariateSmoothing(TestStatesAR3):
    @classmethod
    def setup_class(cls, *args, **kwargs):
        super().setup_class(*args, filter_method=FILTER_UNIVARIATE, **kwargs)

    def test_smooth_method(self):
        assert_equal(self.model.ssm.smooth_method, 0)
        assert_equal(self.model.ssm._kalman_smoother.smooth_method, 0)
        assert_equal(self.model.ssm._kalman_smoother._smooth_method,
                     SMOOTH_UNIVARIATE)


class TestStatesMissingAR3:
    @classmethod
    def setup_class(cls, alternate_timing=False, *args, **kwargs):
        # Dataset
        path = os.path.join(current_path, "results",
                            "results_wpi1_ar3_stata.csv")
        cls.stata = pd.read_csv(path)
        cls.stata.index = pd.date_range(start="1960-01-01", periods=124,
                                        freq="QS")
        # Matlab comparison
        path = os.path.join(current_path, "results",
                            "results_wpi1_missing_ar3_matlab_ssm.csv")
        matlab_names = [
            "a1", "a2", "a3", "detP", "alphahat1", "alphahat2", "alphahat3",
            "detV", "eps", "epsvar", "eta", "etavar"
        ]
        cls.matlab_ssm = pd.read_csv(path, header=None, names=matlab_names)
        # KFAS comparison
        path = os.path.join(current_path, "results",
                            "results_smoothing3_R.csv")
        cls.R_ssm = pd.read_csv(path)

        # Create missing observations
        cls.stata["dwpi"] = cls.stata["wpi"].diff()
        cls.stata.loc[cls.stata.index[10:21], "dwpi"] = np.nan

        cls.model = sarimax.SARIMAX(
            cls.stata.loc[cls.stata.index[1:], "dwpi"],
            *args,
            order=(3, 0, 0),
            hamilton_representation=True,
            **kwargs
        )
        if alternate_timing:
            cls.model.ssm.timing_init_filtered = True

        # Parameters from from Stata's sspace MLE estimation
        params = np.r_[.5270715, .0952613, .2580355, .5307459]
        cls.results = cls.model.smooth(params, return_ssm=True)

        # Calculate the determinant of the covariance matrices (for easy
        # comparison to other languages without having to store 2-dim arrays)
        cls.results.det_predicted_state_cov = np.zeros((1, cls.model.nobs))
        cls.results.det_smoothed_state_cov = np.zeros((1, cls.model.nobs))
        for i in range(cls.model.nobs):
            cls.results.det_predicted_state_cov[0, i] = np.linalg.det(
                cls.results.predicted_state_cov[:, :, i])
            cls.results.det_smoothed_state_cov[0, i] = np.linalg.det(
                cls.results.smoothed_state_cov[:, :, i])

        # Perform simulation smoothing
        nobs = cls.model.nobs
        k_endog = cls.model.k_endog
        k_posdef = cls.model.ssm.k_posdef
        cls.sim = cls.model.simulation_smoother()
        cls.sim.simulate(
            measurement_disturbance_variates=np.zeros(nobs * k_endog),
            state_disturbance_variates=np.zeros(nobs * k_posdef),
            initial_state_variates=np.zeros(cls.model.k_states)
        )

    def test_predicted_states(self):
        assert_almost_equal(
            self.results.predicted_state[:, :-1].T,
            self.matlab_ssm[["a1", "a2", "a3"]], 4
        )

    def test_predicted_states_cov(self):
        assert_almost_equal(
            self.results.det_predicted_state_cov.T,
            self.matlab_ssm[["detP"]], 4
        )

    def test_smoothed_states(self):
        assert_almost_equal(
            self.results.smoothed_state.T,
            self.matlab_ssm[["alphahat1", "alphahat2", "alphahat3"]], 4
        )

    def test_smoothed_states_cov(self):
        assert_almost_equal(
            self.results.det_smoothed_state_cov.T,
            self.matlab_ssm[["detV"]], 4
        )

    def test_smoothed_measurement_disturbance(self):
        assert_almost_equal(
            self.results.smoothed_measurement_disturbance.T,
            self.matlab_ssm[["eps"]], 4
        )

    def test_smoothed_measurement_disturbance_cov(self):
        assert_almost_equal(
            self.results.smoothed_measurement_disturbance_cov[0].T,
            self.matlab_ssm[["epsvar"]], 4
        )

    # There is a discrepancy between MATLAB ssm toolbox and
    # statsmodels.tsa.statespace on the following variables in the case of
    # missing data. Tests against the R package KFAS confirm our results

    def test_smoothed_state_disturbance(self):
        # See note above about why this assertion is invalid
        # assert_almost_equal(
        #     self.results.smoothed_state_disturbance.T,
        #     self.matlab_ssm[['eta']], 4
        # )
        assert_almost_equal(
            self.results.smoothed_state_disturbance.T,
            self.R_ssm[["etahat"]], 9
        )

    def test_smoothed_state_disturbance_cov(self):
        # See note above about why this assertion is invalid
        # assert_almost_equal(
        #     self.results.smoothed_state_disturbance_cov[0].T,
        #     self.matlab_ssm[['etavar']], 4
        # )
        assert_almost_equal(
            self.results.smoothed_state_disturbance_cov[0, 0, :],
            self.R_ssm["detVeta"], 9
        )


class TestStatesMissingAR3AlternateTiming(TestStatesMissingAR3):
    @classmethod
    def setup_class(cls, *args, **kwargs):
        super().setup_class(*args, alternate_timing=True, **kwargs)


class TestStatesMissingAR3AlternativeSmoothing(TestStatesMissingAR3):
    @classmethod
    def setup_class(cls, *args, **kwargs):
        super().setup_class(*args, smooth_method=SMOOTH_ALTERNATIVE, **kwargs)

    def test_smooth_method(self):
        assert_equal(self.model.ssm.smooth_method, SMOOTH_ALTERNATIVE)
        assert_equal(self.model.ssm._kalman_smoother.smooth_method,
                     SMOOTH_ALTERNATIVE)
        assert_equal(self.model.ssm._kalman_smoother._smooth_method,
                     SMOOTH_ALTERNATIVE)


class TestStatesMissingAR3UnivariateSmoothing(TestStatesMissingAR3):
    @classmethod
    def setup_class(cls, *args, **kwargs):
        super().setup_class(*args, filter_method=FILTER_UNIVARIATE, **kwargs)

    def test_smooth_method(self):
        assert_equal(self.model.ssm.smooth_method, 0)
        assert_equal(self.model.ssm._kalman_smoother.smooth_method, 0)
        assert_equal(self.model.ssm._kalman_smoother._smooth_method,
                     SMOOTH_UNIVARIATE)


class TestMultivariateMissing:
    """
    Tests for most filtering and smoothing variables against output from the
    R library KFAS.

    Note that KFAS uses the univariate approach which generally will result in
    different predicted values and covariance matrices associated with the
    measurement equation (e.g. forecasts, etc.). In this case, although the
    model is multivariate, each of the series is truly independent so the
    values will be the same regardless of whether the univariate approach
    is used or not.
    """
    @classmethod
    def setup_class(cls, **kwargs):
        # Results
        path = os.path.join(current_path, "results", "results_smoothing_R.csv")
        cls.desired = pd.read_csv(path)

        # Data
        dta = datasets.macrodata.load_pandas().data
        dta.index = pd.date_range(start="1959-01-01", end="2009-7-01",
                                  freq="QS")
        obs = dta[["realgdp", "realcons", "realinv"]].diff().iloc[1:]
        obs.iloc[0:50, 0] = np.nan
        obs.iloc[19:70, 1] = np.nan
        obs.iloc[39:90, 2] = np.nan
        obs.iloc[119:130, 0] = np.nan
        obs.iloc[119:130, 2] = np.nan

        # Create the model
        mod = mlemodel.MLEModel(obs, k_states=3, k_posdef=3, **kwargs)
        mod["design"] = np.eye(3)
        mod["obs_cov"] = np.eye(3)
        mod["transition"] = np.eye(3)
        mod["selection"] = np.eye(3)
        mod["state_cov"] = np.eye(3)
        mod.initialize_approximate_diffuse(1e6)
        cls.model = mod
        cls.results = mod.smooth([], return_ssm=True)

        # Calculate the determinant of the covariance matrices (for easy
        # comparison to other languages without having to store 2-dim arrays)
        cls.results.det_scaled_smoothed_estimator_cov = (
            np.zeros((1, cls.model.nobs)))
        cls.results.det_predicted_state_cov = np.zeros((1, cls.model.nobs))
        cls.results.det_smoothed_state_cov = np.zeros((1, cls.model.nobs))
        cls.results.det_smoothed_state_disturbance_cov = (
            np.zeros((1, cls.model.nobs)))

        for i in range(cls.model.nobs):
            cls.results.det_scaled_smoothed_estimator_cov[0, i] = (
                np.linalg.det(
                    cls.results.scaled_smoothed_estimator_cov[:, :, i]))
            cls.results.det_predicted_state_cov[0, i] = np.linalg.det(
                cls.results.predicted_state_cov[:, :, i+1])
            cls.results.det_smoothed_state_cov[0, i] = np.linalg.det(
                cls.results.smoothed_state_cov[:, :, i])
            cls.results.det_smoothed_state_disturbance_cov[0, i] = (
                np.linalg.det(
                    cls.results.smoothed_state_disturbance_cov[:, :, i]))

    def test_loglike(self):
        assert_allclose(np.sum(self.results.llf_obs), -205310.9767)

    def test_scaled_smoothed_estimator(self):
        assert_allclose(
            self.results.scaled_smoothed_estimator.T,
            self.desired[["r1", "r2", "r3"]]
        )

    def test_scaled_smoothed_estimator_cov(self):
        assert_allclose(
            self.results.det_scaled_smoothed_estimator_cov.T,
            self.desired[["detN"]]
        )

    def test_forecasts(self):
        assert_allclose(
            self.results.forecasts.T,
            self.desired[["m1", "m2", "m3"]]
        )

    def test_forecasts_error(self):
        assert_allclose(
            self.results.forecasts_error.T,
            self.desired[["v1", "v2", "v3"]]
        )

    def test_forecasts_error_cov(self):
        assert_allclose(
            self.results.forecasts_error_cov.diagonal(),
            self.desired[["F1", "F2", "F3"]]
        )

    def test_predicted_states(self):
        assert_allclose(
            self.results.predicted_state[:, 1:].T,
            self.desired[["a1", "a2", "a3"]]
        )

    def test_predicted_states_cov(self):
        assert_allclose(
            self.results.det_predicted_state_cov.T,
            self.desired[["detP"]]
        )

    def test_smoothed_states(self):
        assert_allclose(
            self.results.smoothed_state.T,
            self.desired[["alphahat1", "alphahat2", "alphahat3"]]
        )

    def test_smoothed_states_cov(self):
        assert_allclose(
            self.results.det_smoothed_state_cov.T,
            self.desired[["detV"]]
        )

    def test_smoothed_forecasts(self):
        assert_allclose(
            self.results.smoothed_forecasts.T,
            self.desired[["muhat1", "muhat2", "muhat3"]]
        )

    def test_smoothed_state_disturbance(self):
        assert_allclose(
            self.results.smoothed_state_disturbance.T,
            self.desired[["etahat1", "etahat2", "etahat3"]]
        )

    def test_smoothed_state_disturbance_cov(self):
        assert_allclose(
            self.results.det_smoothed_state_disturbance_cov.T,
            self.desired[["detVeta"]]
        )

    def test_smoothed_measurement_disturbance(self):
        assert_allclose(
            self.results.smoothed_measurement_disturbance.T,
            self.desired[["epshat1", "epshat2", "epshat3"]]
        )

    def test_smoothed_measurement_disturbance_cov(self):
        assert_allclose(
            self.results.smoothed_measurement_disturbance_cov.diagonal(),
            self.desired[["Veps1", "Veps2", "Veps3"]]
        )


class TestMultivariateMissingClassicalSmoothing(TestMultivariateMissing):
    @classmethod
    def setup_class(cls, *args, **kwargs):
        super().setup_class(*args, smooth_method=SMOOTH_CLASSICAL, **kwargs)

    def test_smooth_method(self):
        assert_equal(self.model.ssm.smooth_method, SMOOTH_CLASSICAL)
        assert_equal(self.model.ssm._kalman_smoother.smooth_method,
                     SMOOTH_CLASSICAL)
        assert_equal(self.model.ssm._kalman_smoother._smooth_method,
                     SMOOTH_CLASSICAL)


class TestMultivariateMissingAlternativeSmoothing(TestMultivariateMissing):
    @classmethod
    def setup_class(cls, *args, **kwargs):
        super().setup_class(*args, smooth_method=SMOOTH_ALTERNATIVE, **kwargs)

    def test_smooth_method(self):
        assert_equal(self.model.ssm.smooth_method, SMOOTH_ALTERNATIVE)
        assert_equal(self.model.ssm._kalman_smoother.smooth_method,
                     SMOOTH_ALTERNATIVE)
        assert_equal(self.model.ssm._kalman_smoother._smooth_method,
                     SMOOTH_ALTERNATIVE)


class TestMultivariateMissingUnivariateSmoothing(TestMultivariateMissing):
    @classmethod
    def setup_class(cls, **kwargs):
        super().setup_class(filter_method=FILTER_UNIVARIATE, **kwargs)

    def test_smooth_method(self):
        assert_equal(self.model.ssm.smooth_method, 0)
        assert_equal(self.model.ssm._kalman_smoother.smooth_method, 0)
        assert_equal(self.model.ssm._kalman_smoother._smooth_method,
                     SMOOTH_UNIVARIATE)


class TestMultivariateVAR:
    """
    Tests for most filtering and smoothing variables against output from the
    R library KFAS.

    Note that KFAS uses the univariate approach which generally will result in
    different predicted values and covariance matrices associated with the
    measurement equation (e.g. forecasts, etc.). In this case, although the
    model is multivariate, each of the series is truly independent so the
    values will be the same regardless of whether the univariate approach is
    used or not.
    """
    @classmethod
    def setup_class(cls, *args, **kwargs):
        # Results
        path = os.path.join(current_path, "results",
                            "results_smoothing2_R.csv")
        cls.desired = pd.read_csv(path)

        # Data
        dta = datasets.macrodata.load_pandas().data
        dta.index = pd.date_range(start="1959-01-01", end="2009-7-01",
                                  freq="QS")
        obs = np.log(dta[["realgdp", "realcons", "realinv"]]).diff().iloc[1:]

        # Create the model
        mod = mlemodel.MLEModel(obs, k_states=3, k_posdef=3, **kwargs)
        mod["design"] = np.eye(3)
        mod["obs_cov"] = np.array([
            [0.0000640649,  0.,            0.],
            [0.,            0.0000572802,  0.],
            [0.,            0.,            0.0017088585]])
        mod["transition"] = np.array([
            [-0.1119908792,  0.8441841604,  0.0238725303],
            [0.2629347724,   0.4996718412, -0.0173023305],
            [-3.2192369082,  4.1536028244,  0.4514379215]])
        mod["selection"] = np.eye(3)
        mod["state_cov"] = np.array([
            [0.0000640649,  0.0000388496,  0.0002148769],
            [0.0000388496,  0.0000572802,  0.000001555],
            [0.0002148769,  0.000001555,   0.0017088585]])
        mod.initialize_approximate_diffuse(1e6)
        cls.model = mod
        cls.results = mod.smooth([], return_ssm=True)

        # Calculate the determinant of the covariance matrices (for easy
        # comparison to other languages without having to store 2-dim arrays)
        cls.results.det_scaled_smoothed_estimator_cov = (
            np.zeros((1, cls.model.nobs)))
        cls.results.det_predicted_state_cov = np.zeros((1, cls.model.nobs))
        cls.results.det_smoothed_state_cov = np.zeros((1, cls.model.nobs))
        cls.results.det_smoothed_state_disturbance_cov = (
            np.zeros((1, cls.model.nobs)))

        for i in range(cls.model.nobs):
            cls.results.det_scaled_smoothed_estimator_cov[0, i] = (
                np.linalg.det(
                    cls.results.scaled_smoothed_estimator_cov[:, :, i]))
            cls.results.det_predicted_state_cov[0, i] = np.linalg.det(
                cls.results.predicted_state_cov[:, :, i+1])
            cls.results.det_smoothed_state_cov[0, i] = np.linalg.det(
                cls.results.smoothed_state_cov[:, :, i])
            cls.results.det_smoothed_state_disturbance_cov[0, i] = (
                np.linalg.det(
                    cls.results.smoothed_state_disturbance_cov[:, :, i]))

    def test_loglike(self):
        assert_allclose(np.sum(self.results.llf_obs), 1695.34872)

    def test_scaled_smoothed_estimator(self):
        assert_allclose(
            self.results.scaled_smoothed_estimator.T,
            self.desired[["r1", "r2", "r3"]], atol=1e-4
        )

    def test_scaled_smoothed_estimator_cov(self):
        # Last obs is zero, so exclude it
        assert_allclose(
            np.log(self.results.det_scaled_smoothed_estimator_cov.T[:-1]),
            np.log(self.desired[["detN"]][:-1]), atol=1e-6
        )

    def test_forecasts(self):
        assert_allclose(
            self.results.forecasts.T,
            self.desired[["m1", "m2", "m3"]], atol=1e-6
        )

    def test_forecasts_error(self):
        assert_allclose(
            self.results.forecasts_error.T[:, 0],
            self.desired["v1"], atol=1e-6
        )

    def test_forecasts_error_cov(self):
        assert_allclose(
            self.results.forecasts_error_cov.diagonal()[:, 0],
            self.desired["F1"], atol=1e-6
        )

    def test_predicted_states(self):
        assert_allclose(
            self.results.predicted_state[:, 1:].T,
            self.desired[["a1", "a2", "a3"]], atol=1e-6
        )

    def test_predicted_states_cov(self):
        assert_allclose(
            self.results.det_predicted_state_cov.T,
            self.desired[["detP"]], atol=1e-16
        )

    def test_smoothed_states(self):
        assert_allclose(
            self.results.smoothed_state.T,
            self.desired[["alphahat1", "alphahat2", "alphahat3"]], atol=1e-6
        )

    def test_smoothed_states_cov(self):
        assert_allclose(
            self.results.det_smoothed_state_cov.T,
            self.desired[["detV"]], atol=1e-16
        )

    def test_smoothed_forecasts(self):
        assert_allclose(
            self.results.smoothed_forecasts.T,
            self.desired[["muhat1", "muhat2", "muhat3"]], atol=1e-6
        )

    def test_smoothed_state_disturbance(self):
        assert_allclose(
            self.results.smoothed_state_disturbance.T,
            self.desired[["etahat1", "etahat2", "etahat3"]], atol=1e-6
        )

    def test_smoothed_state_disturbance_cov(self):
        assert_allclose(
            self.results.det_smoothed_state_disturbance_cov.T,
            self.desired[["detVeta"]], atol=1e-18
        )

    def test_smoothed_measurement_disturbance(self):
        assert_allclose(
            self.results.smoothed_measurement_disturbance.T,
            self.desired[["epshat1", "epshat2", "epshat3"]], atol=1e-6
        )

    def test_smoothed_measurement_disturbance_cov(self):
        assert_allclose(
            self.results.smoothed_measurement_disturbance_cov.diagonal(),
            self.desired[["Veps1", "Veps2", "Veps3"]], atol=1e-6
        )


class TestMultivariateVARAlternativeSmoothing(TestMultivariateVAR):
    @classmethod
    def setup_class(cls, *args, **kwargs):
        super().setup_class(*args, smooth_method=SMOOTH_ALTERNATIVE, **kwargs)

    def test_smooth_method(self):
        assert_equal(self.model.ssm.smooth_method, SMOOTH_ALTERNATIVE)
        assert_equal(self.model.ssm._kalman_smoother.smooth_method,
                     SMOOTH_ALTERNATIVE)
        assert_equal(self.model.ssm._kalman_smoother._smooth_method,
                     SMOOTH_ALTERNATIVE)


class TestMultivariateVARClassicalSmoothing(TestMultivariateVAR):
    @classmethod
    def setup_class(cls, *args, **kwargs):
        super().setup_class(*args, smooth_method=SMOOTH_CLASSICAL, **kwargs)

    def test_smooth_method(self):
        assert_equal(self.model.ssm.smooth_method, SMOOTH_CLASSICAL)
        assert_equal(self.model.ssm._kalman_smoother.smooth_method,
                     SMOOTH_CLASSICAL)
        assert_equal(self.model.ssm._kalman_smoother._smooth_method,
                     SMOOTH_CLASSICAL)


class TestMultivariateVARUnivariate:
    """
    Tests for most filtering and smoothing variables against output from the
    R library KFAS.

    Note that KFAS uses the univariate approach which generally will result in
    different predicted values and covariance matrices associated with the
    measurement equation (e.g. forecasts, etc.). In this case, although the
    model is multivariate, each of the series is truly independent so the
    values will be the same regardless of whether the univariate approach is
    used or not.
    """
    @classmethod
    def setup_class(cls, *args, **kwargs):
        # Results
        path = os.path.join(current_path, "results",
                            "results_smoothing2_R.csv")
        cls.desired = pd.read_csv(path)

        # Data
        dta = datasets.macrodata.load_pandas().data
        dta.index = pd.date_range(start="1959-01-01", end="2009-7-01",
                                  freq="QS")
        obs = np.log(dta[["realgdp", "realcons", "realinv"]]).diff().iloc[1:]

        # Create the model
        mod = mlemodel.MLEModel(obs, k_states=3, k_posdef=3, **kwargs)
        mod.ssm.filter_univariate = True
        mod["design"] = np.eye(3)
        mod["obs_cov"] = np.array([
            [0.0000640649,  0.,            0.],
            [0.,            0.0000572802,  0.],
            [0.,            0.,            0.0017088585]])
        mod["transition"] = np.array([
            [-0.1119908792,  0.8441841604,  0.0238725303],
            [0.2629347724,   0.4996718412, -0.0173023305],
            [-3.2192369082,  4.1536028244,  0.4514379215]])
        mod["selection"] = np.eye(3)
        mod["state_cov"] = np.array([
            [0.0000640649,  0.0000388496,  0.0002148769],
            [0.0000388496,  0.0000572802,  0.000001555],
            [0.0002148769,  0.000001555,   0.0017088585]])
        mod.initialize_approximate_diffuse(1e6)
        cls.model = mod
        cls.results = mod.smooth([], return_ssm=True)

        # Calculate the determinant of the covariance matrices (for easy
        # comparison to other languages without having to store 2-dim arrays)
        cls.results.det_scaled_smoothed_estimator_cov = (
            np.zeros((1, cls.model.nobs)))
        cls.results.det_predicted_state_cov = np.zeros((1, cls.model.nobs))
        cls.results.det_smoothed_state_cov = np.zeros((1, cls.model.nobs))
        cls.results.det_smoothed_state_disturbance_cov = (
            np.zeros((1, cls.model.nobs)))

        for i in range(cls.model.nobs):
            cls.results.det_scaled_smoothed_estimator_cov[0, i] = (
                np.linalg.det(
                    cls.results.scaled_smoothed_estimator_cov[:, :, i]))
            cls.results.det_predicted_state_cov[0, i] = np.linalg.det(
                cls.results.predicted_state_cov[:, :, i+1])
            cls.results.det_smoothed_state_cov[0, i] = np.linalg.det(
                cls.results.smoothed_state_cov[:, :, i])
            cls.results.det_smoothed_state_disturbance_cov[0, i] = (
                np.linalg.det(
                    cls.results.smoothed_state_disturbance_cov[:, :, i]))

    def test_loglike(self):
        assert_allclose(np.sum(self.results.llf_obs), 1695.34872)

    def test_scaled_smoothed_estimator(self):
        assert_allclose(
            self.results.scaled_smoothed_estimator.T,
            self.desired[["r1", "r2", "r3"]], atol=1e-4
        )

    def test_scaled_smoothed_estimator_cov(self):
        # Last obs is zero, so exclude it
        assert_allclose(
            np.log(self.results.det_scaled_smoothed_estimator_cov.T[:-1]),
            np.log(self.desired[["detN"]][:-1])
        )

    def test_forecasts(self):
        assert_allclose(
            self.results.forecasts.T[:, 0],
            self.desired["m1"], atol=1e-6
        )

    def test_forecasts_error(self):
        assert_allclose(
            self.results.forecasts_error.T,
            self.desired[["v1", "v2", "v3"]], atol=1e-6
        )

    def test_forecasts_error_cov(self):
        assert_allclose(
            self.results.forecasts_error_cov.diagonal(),
            self.desired[["F1", "F2", "F3"]]
        )

    def test_predicted_states(self):
        assert_allclose(
            self.results.predicted_state[:, 1:].T,
            self.desired[["a1", "a2", "a3"]], atol=1e-8
        )

    def test_predicted_states_cov(self):
        assert_allclose(
            self.results.det_predicted_state_cov.T,
            self.desired[["detP"]], atol=1e-18
        )

    def test_smoothed_states(self):
        assert_allclose(
            self.results.smoothed_state.T,
            self.desired[["alphahat1", "alphahat2", "alphahat3"]], atol=1e-6
        )

    def test_smoothed_states_cov(self):
        assert_allclose(
            self.results.det_smoothed_state_cov.T,
            self.desired[["detV"]], atol=1e-18
        )

    def test_smoothed_forecasts(self):
        assert_allclose(
            self.results.smoothed_forecasts.T,
            self.desired[["muhat1", "muhat2", "muhat3"]], atol=1e-6
        )

    def test_smoothed_state_disturbance(self):
        assert_allclose(
