reconnect moved files to git repo

venv/lib/python3.11/site-packages/statsmodels/tsa/regime_switching/__init__.py

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+from statsmodels.tools._test_runner import PytestTester
+
+test = PytestTester()

venv/lib/python3.11/site-packages/statsmodels/tsa/regime_switching/markov_autoregression.py

@@ -0,0 +1,493 @@
+"""
+Markov switching autoregression models
+
+Author: Chad Fulton
+License: BSD-3
+"""
+
+
+import numpy as np
+import statsmodels.base.wrapper as wrap
+
+from statsmodels.tsa.tsatools import lagmat
+from statsmodels.tsa.regime_switching import (
+    markov_switching, markov_regression)
+from statsmodels.tsa.statespace.tools import (
+    constrain_stationary_univariate, unconstrain_stationary_univariate)
+
+
+class MarkovAutoregression(markov_regression.MarkovRegression):
+    r"""
+    Markov switching regression model
+
+    Parameters
+    ----------
+    endog : array_like
+        The endogenous variable.
+    k_regimes : int
+        The number of regimes.
+    order : int
+        The order of the autoregressive lag polynomial.
+    trend : {'n', 'c', 't', 'ct'}
+        Whether or not to include a trend. To include an constant, time trend,
+        or both, set `trend='c'`, `trend='t'`, or `trend='ct'`. For no trend,
+        set `trend='n'`. Default is a constant.
+    exog : array_like, optional
+        Array of exogenous regressors, shaped nobs x k.
+    exog_tvtp : array_like, optional
+        Array of exogenous or lagged variables to use in calculating
+        time-varying transition probabilities (TVTP). TVTP is only used if this
+        variable is provided. If an intercept is desired, a column of ones must
+        be explicitly included in this array.
+    switching_ar : bool or iterable, optional
+        If a boolean, sets whether or not all autoregressive coefficients are
+        switching across regimes. If an iterable, should be of length equal
+        to `order`, where each element is a boolean describing whether the
+        corresponding coefficient is switching. Default is True.
+    switching_trend : bool or iterable, optional
+        If a boolean, sets whether or not all trend coefficients are
+        switching across regimes. If an iterable, should be of length equal
+        to the number of trend variables, where each element is
+        a boolean describing whether the corresponding coefficient is
+        switching. Default is True.
+    switching_exog : bool or iterable, optional
+        If a boolean, sets whether or not all regression coefficients are
+        switching across regimes. If an iterable, should be of length equal
+        to the number of exogenous variables, where each element is
+        a boolean describing whether the corresponding coefficient is
+        switching. Default is True.
+    switching_variance : bool, optional
+        Whether or not there is regime-specific heteroskedasticity, i.e.
+        whether or not the error term has a switching variance. Default is
+        False.
+
+    Notes
+    -----
+    This model is new and API stability is not guaranteed, although changes
+    will be made in a backwards compatible way if possible.
+
+    The model can be written as:
+
+    .. math::
+
+        y_t = a_{S_t} + x_t' \beta_{S_t} + \phi_{1, S_t}
+        (y_{t-1} - a_{S_{t-1}} - x_{t-1}' \beta_{S_{t-1}}) + \dots +
+        \phi_{p, S_t} (y_{t-p} - a_{S_{t-p}} - x_{t-p}' \beta_{S_{t-p}}) +
+        \varepsilon_t \\
+        \varepsilon_t \sim N(0, \sigma_{S_t}^2)
+
+    i.e. the model is an autoregression with where the autoregressive
+    coefficients, the mean of the process (possibly including trend or
+    regression effects) and the variance of the error term may be switching
+    across regimes.
+
+    The `trend` is accommodated by prepending columns to the `exog` array. Thus
+    if `trend='c'`, the passed `exog` array should not already have a column of
+    ones.
+
+    See the notebook `Markov switching autoregression
+    <../examples/notebooks/generated/markov_autoregression.html>`__
+    for an overview.
+
+    References
+    ----------
+    Kim, Chang-Jin, and Charles R. Nelson. 1999.
+    "State-Space Models with Regime Switching:
+    Classical and Gibbs-Sampling Approaches with Applications".
+    MIT Press Books. The MIT Press.
+    """
+
+    def __init__(self, endog, k_regimes, order, trend='c', exog=None,
+                 exog_tvtp=None, switching_ar=True, switching_trend=True,
+                 switching_exog=False, switching_variance=False,
+                 dates=None, freq=None, missing='none'):
+
+        # Properties
+        self.switching_ar = switching_ar
+
+        # Switching options
+        if self.switching_ar is True or self.switching_ar is False:
+            self.switching_ar = [self.switching_ar] * order
+        elif not len(self.switching_ar) == order:
+            raise ValueError('Invalid iterable passed to `switching_ar`.')
+
+        # Initialize the base model
+        super().__init__(
+            endog, k_regimes, trend=trend, exog=exog, order=order,
+            exog_tvtp=exog_tvtp, switching_trend=switching_trend,
+            switching_exog=switching_exog,
+            switching_variance=switching_variance, dates=dates, freq=freq,
+            missing=missing)
+
+        # Sanity checks
+        if self.nobs <= self.order:
+            raise ValueError('Must have more observations than the order of'
+                             ' the autoregression.')
+
+        # Autoregressive exog
+        self.exog_ar = lagmat(endog, self.order)[self.order:]
+
+        # Reshape other datasets
+        self.nobs -= self.order
+        self.orig_endog = self.endog
+        self.endog = self.endog[self.order:]
+        if self._k_exog > 0:
+            self.orig_exog = self.exog
+            self.exog = self.exog[self.order:]
+
+        # Reset the ModelData datasets
+        self.data.endog, self.data.exog = (
+            self.data._convert_endog_exog(self.endog, self.exog))
+
+        # Reset indexes, if provided
+        if self.data.row_labels is not None:
+            self.data._cache['row_labels'] = (
+                self.data.row_labels[self.order:])
+        if self._index is not None:
+            if self._index_generated:
+                self._index = self._index[:-self.order]
+            else:
+                self._index = self._index[self.order:]
+
+        # Parameters
+        self.parameters['autoregressive'] = self.switching_ar
+
+        # Cache an array for holding slices
+        self._predict_slices = [slice(None, None, None)] * (self.order + 1)
+
+    def predict_conditional(self, params):
+        """
+        In-sample prediction, conditional on the current and previous regime
+
+        Parameters
+        ----------
+        params : array_like
+            Array of parameters at which to create predictions.
+
+        Returns
+        -------
+        predict : array_like
+            Array of predictions conditional on current, and possibly past,
+            regimes
+        """
+        params = np.array(params, ndmin=1)
+
+        # Prediction is based on:
+        # y_t = x_t beta^{(S_t)} +
+        #       \phi_1^{(S_t)} (y_{t-1} - x_{t-1} beta^{(S_t-1)}) + ...
+        #       \phi_p^{(S_t)} (y_{t-p} - x_{t-p} beta^{(S_t-p)}) + eps_t
+        if self._k_exog > 0:
+            xb = []
+            for i in range(self.k_regimes):
+                coeffs = params[self.parameters[i, 'exog']]
+                xb.append(np.dot(self.orig_exog, coeffs))
+
+        predict = np.zeros(
+            (self.k_regimes,) * (self.order + 1) + (self.nobs,),
+            dtype=np.promote_types(np.float64, params.dtype))
+        # Iterate over S_{t} = i
+        for i in range(self.k_regimes):
+            ar_coeffs = params[self.parameters[i, 'autoregressive']]
+
+            # y_t - x_t beta^{(S_t)}
+            ix = self._predict_slices[:]
+            ix[0] = i
+            ix = tuple(ix)
+            if self._k_exog > 0:
+                predict[ix] += xb[i][self.order:]
+
+            # Iterate over j = 2, .., p
+            for j in range(1, self.order + 1):
+                for k in range(self.k_regimes):
+                    # This gets a specific time-period / regime slice:
+                    # S_{t} = i, S_{t-j} = k, across all other time-period /
+                    # regime slices.
+                    ix = self._predict_slices[:]
+                    ix[0] = i
+                    ix[j] = k
+                    ix = tuple(ix)
+
+                    start = self.order - j
+                    end = -j
+                    if self._k_exog > 0:
+                        predict[ix] += ar_coeffs[j-1] * (
+                            self.orig_endog[start:end] - xb[k][start:end])
+                    else:
+                        predict[ix] += ar_coeffs[j-1] * (
+                            self.orig_endog[start:end])
+
+        return predict
+
+    def _resid(self, params):
+        return self.endog - self.predict_conditional(params)
+
+    def _conditional_loglikelihoods(self, params):
+        """
+        Compute loglikelihoods conditional on the current period's regime and
+        the last `self.order` regimes.
+        """
+        # Get the residuals
+        resid = self._resid(params)
+
+        # Compute the conditional likelihoods
+        variance = params[self.parameters['variance']].squeeze()
+        if self.switching_variance:
+            variance = np.reshape(variance, (self.k_regimes, 1, 1))
+
+        conditional_loglikelihoods = (
+            -0.5 * resid**2 / variance - 0.5 * np.log(2 * np.pi * variance))
+
+        return conditional_loglikelihoods
+
+    @property
+    def _res_classes(self):
+        return {'fit': (MarkovAutoregressionResults,
+                        MarkovAutoregressionResultsWrapper)}
+
+    def _em_iteration(self, params0):
+        """
+        EM iteration
+        """
+        # Inherited parameters
+        result, params1 = markov_switching.MarkovSwitching._em_iteration(
+            self, params0)
+
+        tmp = np.sqrt(result.smoothed_marginal_probabilities)
+
+        # Regression coefficients
+        coeffs = None
+        if self._k_exog > 0:
+            coeffs = self._em_exog(result, self.endog, self.exog,
+                                   self.parameters.switching['exog'], tmp)
+            for i in range(self.k_regimes):
+                params1[self.parameters[i, 'exog']] = coeffs[i]
+
+        # Autoregressive
+        if self.order > 0:
+            if self._k_exog > 0:
+                ar_coeffs, variance = self._em_autoregressive(
+                    result, coeffs)
+            else:
+                ar_coeffs = self._em_exog(
+                    result, self.endog, self.exog_ar,
+                    self.parameters.switching['autoregressive'])
+                variance = self._em_variance(
+                    result, self.endog, self.exog_ar, ar_coeffs, tmp)
+            for i in range(self.k_regimes):
+                params1[self.parameters[i, 'autoregressive']] = ar_coeffs[i]
+            params1[self.parameters['variance']] = variance
+
+        return result, params1
+
+    def _em_autoregressive(self, result, betas, tmp=None):
+        """
+        EM step for autoregressive coefficients and variances
+        """
+        if tmp is None:
+            tmp = np.sqrt(result.smoothed_marginal_probabilities)
+
+        resid = np.zeros((self.k_regimes, self.nobs + self.order))
+        resid[:] = self.orig_endog
+        if self._k_exog > 0:
+            for i in range(self.k_regimes):
+                resid[i] -= np.dot(self.orig_exog, betas[i])
+
+        # The difference between this and `_em_exog` is that here we have a
+        # different endog and exog for each regime
+        coeffs = np.zeros((self.k_regimes,) + (self.order,))
+        variance = np.zeros((self.k_regimes,))
+        exog = np.zeros((self.nobs, self.order))
+        for i in range(self.k_regimes):
+            endog = resid[i, self.order:]
+            exog = lagmat(resid[i], self.order)[self.order:]
+            tmp_endog = tmp[i] * endog
+            tmp_exog = tmp[i][:, None] * exog
+
+            coeffs[i] = np.dot(np.linalg.pinv(tmp_exog), tmp_endog)
+
+            if self.switching_variance:
+                tmp_resid = endog - np.dot(exog, coeffs[i])
+                variance[i] = (np.sum(
+                    tmp_resid**2 * result.smoothed_marginal_probabilities[i]) /
+                    np.sum(result.smoothed_marginal_probabilities[i]))
+            else:
+                tmp_resid = tmp_endog - np.dot(tmp_exog, coeffs[i])
+                variance[i] = np.sum(tmp_resid**2)
+
+        # Variances
+        if not self.switching_variance:
+            variance = variance.sum() / self.nobs
+
+        return coeffs, variance
+
+    @property
+    def start_params(self):
+        """
+        (array) Starting parameters for maximum likelihood estimation.
+        """
+        # Inherited parameters
+        params = markov_switching.MarkovSwitching.start_params.fget(self)
+
+        # OLS for starting parameters
+        endog = self.endog.copy()
+        if self._k_exog > 0 and self.order > 0:
+            exog = np.c_[self.exog, self.exog_ar]
+        elif self._k_exog > 0:
+            exog = self.exog
+        elif self.order > 0:
+            exog = self.exog_ar
+
+        if self._k_exog > 0 or self.order > 0:
+            beta = np.dot(np.linalg.pinv(exog), endog)
+            variance = np.var(endog - np.dot(exog, beta))
+        else:
+            variance = np.var(endog)
+
+        # Regression coefficients
+        if self._k_exog > 0:
+            if np.any(self.switching_coeffs):
+                for i in range(self.k_regimes):
+                    params[self.parameters[i, 'exog']] = (
+                        beta[:self._k_exog] * (i / self.k_regimes))
+            else:
+                params[self.parameters['exog']] = beta[:self._k_exog]
+
+        # Autoregressive
+        if self.order > 0:
+            if np.any(self.switching_ar):
+                for i in range(self.k_regimes):
+                    params[self.parameters[i, 'autoregressive']] = (
+                        beta[self._k_exog:] * (i / self.k_regimes))
+            else:
+                params[self.parameters['autoregressive']] = beta[self._k_exog:]
+
+        # Variance
+        if self.switching_variance:
+            params[self.parameters['variance']] = (
+                np.linspace(variance / 10., variance, num=self.k_regimes))
+        else:
+            params[self.parameters['variance']] = variance
+
+        return params
+
+    @property
+    def param_names(self):
+        """
+        (list of str) List of human readable parameter names (for parameters
+        actually included in the model).
+        """
+        # Inherited parameters
+        param_names = np.array(
+            markov_regression.MarkovRegression.param_names.fget(self),
+            dtype=object)
+
+        # Autoregressive
+        if np.any(self.switching_ar):
+            for i in range(self.k_regimes):
+                param_names[self.parameters[i, 'autoregressive']] = [
+                    'ar.L%d[%d]' % (j+1, i) for j in range(self.order)]
+        else:
+            param_names[self.parameters['autoregressive']] = [
+                'ar.L%d' % (j+1) for j in range(self.order)]
+
+        return param_names.tolist()
+
+    def transform_params(self, unconstrained):
+        """
+        Transform unconstrained parameters used by the optimizer to constrained
+        parameters used in likelihood evaluation
+
+        Parameters
+        ----------
+        unconstrained : array_like
+            Array of unconstrained parameters used by the optimizer, to be
+            transformed.
+
+        Returns
+        -------
+        constrained : array_like
+            Array of constrained parameters which may be used in likelihood
+            evaluation.
+        """
+        # Inherited parameters
+        constrained = super().transform_params(
+            unconstrained)
+
+        # Autoregressive
+        # TODO may provide unexpected results when some coefficients are not
+        # switching
+        for i in range(self.k_regimes):
+            s = self.parameters[i, 'autoregressive']
+            constrained[s] = constrain_stationary_univariate(
+                unconstrained[s])
+
+        return constrained
+
+    def untransform_params(self, constrained):
+        """
+        Transform constrained parameters used in likelihood evaluation
+        to unconstrained parameters used by the optimizer
+
+        Parameters
+        ----------
+        constrained : array_like
+            Array of constrained parameters used in likelihood evaluation, to
+            be transformed.
+
+        Returns
+        -------
+        unconstrained : array_like
+            Array of unconstrained parameters used by the optimizer.
+        """
+        # Inherited parameters
+        unconstrained = super().untransform_params(
+            constrained)
+
+        # Autoregressive
+        # TODO may provide unexpected results when some coefficients are not
+        # switching
+        for i in range(self.k_regimes):
+            s = self.parameters[i, 'autoregressive']
+            unconstrained[s] = unconstrain_stationary_univariate(
+                constrained[s])
+
+        return unconstrained
+
+
+class MarkovAutoregressionResults(markov_regression.MarkovRegressionResults):
+    r"""
+    Class to hold results from fitting a Markov switching autoregression model
+
+    Parameters
+    ----------
+    model : MarkovAutoregression instance
+        The fitted model instance
+    params : ndarray
+        Fitted parameters
+    filter_results : HamiltonFilterResults or KimSmootherResults instance
+        The underlying filter and, optionally, smoother output
+    cov_type : str
+        The type of covariance matrix estimator to use. Can be one of 'approx',
+        'opg', 'robust', or 'none'.
+
+    Attributes
+    ----------
+    model : Model instance
+        A reference to the model that was fit.
+    filter_results : HamiltonFilterResults or KimSmootherResults instance
+        The underlying filter and, optionally, smoother output
+    nobs : float
+        The number of observations used to fit the model.
+    params : ndarray
+        The parameters of the model.
+    scale : float
+        This is currently set to 1.0 and not used by the model or its results.
+    """
+    pass
+
+
+class MarkovAutoregressionResultsWrapper(
+        markov_regression.MarkovRegressionResultsWrapper):
+    pass
+wrap.populate_wrapper(MarkovAutoregressionResultsWrapper,  # noqa:E305
+                      MarkovAutoregressionResults)

venv/lib/python3.11/site-packages/statsmodels/tsa/regime_switching/markov_regression.py

@@ -0,0 +1,456 @@
+"""
+Markov switching regression models
+
+Author: Chad Fulton
+License: BSD-3
+"""
+import numpy as np
+import statsmodels.base.wrapper as wrap
+
+from statsmodels.tsa.regime_switching import markov_switching
+
+
+class MarkovRegression(markov_switching.MarkovSwitching):
+    r"""
+    First-order k-regime Markov switching regression model
+
+    Parameters
+    ----------
+    endog : array_like
+        The endogenous variable.
+    k_regimes : int
+        The number of regimes.
+    trend : {'n', 'c', 't', 'ct'}
+        Whether or not to include a trend. To include an intercept, time trend,
+        or both, set `trend='c'`, `trend='t'`, or `trend='ct'`. For no trend,
+        set `trend='n'`. Default is an intercept.
+    exog : array_like, optional
+        Array of exogenous regressors, shaped nobs x k.
+    order : int, optional
+        The order of the model describes the dependence of the likelihood on
+        previous regimes. This depends on the model in question and should be
+        set appropriately by subclasses.
+    exog_tvtp : array_like, optional
+        Array of exogenous or lagged variables to use in calculating
+        time-varying transition probabilities (TVTP). TVTP is only used if this
+        variable is provided. If an intercept is desired, a column of ones must
+        be explicitly included in this array.
+    switching_trend : bool or iterable, optional
+        If a boolean, sets whether or not all trend coefficients are
+        switching across regimes. If an iterable, should be of length equal
+        to the number of trend variables, where each element is
+        a boolean describing whether the corresponding coefficient is
+        switching. Default is True.
+    switching_exog : bool or iterable, optional
+        If a boolean, sets whether or not all regression coefficients are
+        switching across regimes. If an iterable, should be of length equal
+        to the number of exogenous variables, where each element is
+        a boolean describing whether the corresponding coefficient is
+        switching. Default is True.
+    switching_variance : bool, optional
+        Whether or not there is regime-specific heteroskedasticity, i.e.
+        whether or not the error term has a switching variance. Default is
+        False.
+
+    Notes
+    -----
+    This model is new and API stability is not guaranteed, although changes
+    will be made in a backwards compatible way if possible.
+
+    The model can be written as:
+
+    .. math::
+
+        y_t = a_{S_t} + x_t' \beta_{S_t} + \varepsilon_t \\
+        \varepsilon_t \sim N(0, \sigma_{S_t}^2)
+
+    i.e. the model is a dynamic linear regression where the coefficients and
+    the variance of the error term may be switching across regimes.
+
+    The `trend` is accommodated by prepending columns to the `exog` array. Thus
+    if `trend='c'`, the passed `exog` array should not already have a column of
+    ones.
+
+    See the notebook `Markov switching dynamic regression
+    <../examples/notebooks/generated/markov_regression.html>`__ for an
+    overview.
+
+    References
+    ----------
+    Kim, Chang-Jin, and Charles R. Nelson. 1999.
+    "State-Space Models with Regime Switching:
+    Classical and Gibbs-Sampling Approaches with Applications".
+    MIT Press Books. The MIT Press.
+    """
+
+    def __init__(self, endog, k_regimes, trend='c', exog=None, order=0,
+                 exog_tvtp=None, switching_trend=True, switching_exog=True,
+                 switching_variance=False, dates=None, freq=None,
+                 missing='none'):
+
+        # Properties
+        from statsmodels.tools.validation import string_like
+        self.trend = string_like(trend, "trend", options=("n", "c", "ct", "t"))
+        self.switching_trend = switching_trend
+        self.switching_exog = switching_exog
+        self.switching_variance = switching_variance
+
+        # Exogenous data
+        self.k_exog, exog = markov_switching.prepare_exog(exog)
+
+        # Trend
+        nobs = len(endog)
+        self.k_trend = 0
+        self._k_exog = self.k_exog
+        trend_exog = None
+        if trend == 'c':
+            trend_exog = np.ones((nobs, 1))
+            self.k_trend = 1
+        elif trend == 't':
+            trend_exog = (np.arange(nobs) + 1)[:, np.newaxis]
+            self.k_trend = 1
+        elif trend == 'ct':
+            trend_exog = np.c_[np.ones((nobs, 1)),
+                               (np.arange(nobs) + 1)[:, np.newaxis]]
+            self.k_trend = 2
+        if trend_exog is not None:
+            exog = trend_exog if exog is None else np.c_[trend_exog, exog]
+            self._k_exog += self.k_trend
+
+        # Initialize the base model
+        super().__init__(
+            endog, k_regimes, order=order, exog_tvtp=exog_tvtp, exog=exog,
+            dates=dates, freq=freq, missing=missing)
+
+        # Switching options
+        if self.switching_trend is True or self.switching_trend is False:
+            self.switching_trend = [self.switching_trend] * self.k_trend
+        elif not len(self.switching_trend) == self.k_trend:
+            raise ValueError('Invalid iterable passed to `switching_trend`.')
+        if self.switching_exog is True or self.switching_exog is False:
+            self.switching_exog = [self.switching_exog] * self.k_exog
+        elif not len(self.switching_exog) == self.k_exog:
+            raise ValueError('Invalid iterable passed to `switching_exog`.')
+
+        self.switching_coeffs = (
+            np.r_[self.switching_trend,
+                  self.switching_exog].astype(bool).tolist())
+
+        # Parameters
+        self.parameters['exog'] = self.switching_coeffs
+        self.parameters['variance'] = [1] if self.switching_variance else [0]
+
+    def predict_conditional(self, params):
+        """
+        In-sample prediction, conditional on the current regime
+
+        Parameters
+        ----------
+        params : array_like
+            Array of parameters at which to perform prediction.
+
+        Returns
+        -------
+        predict : array_like
+            Array of predictions conditional on current, and possibly past,
+            regimes
+        """
+        params = np.array(params, ndmin=1)
+
+        # Since in the base model the values are the same across columns, we
+        # only compute a single column, and then expand it below.
+        predict = np.zeros((self.k_regimes, self.nobs), dtype=params.dtype)
+
+        for i in range(self.k_regimes):
+            # Predict
+            if self._k_exog > 0:
+                coeffs = params[self.parameters[i, 'exog']]
+                predict[i] = np.dot(self.exog, coeffs)
+
+        return predict[:, None, :]
+
+    def _resid(self, params):
+        predict = np.repeat(self.predict_conditional(params),
+                            self.k_regimes, axis=1)
+        return self.endog - predict
+
+    def _conditional_loglikelihoods(self, params):
+        """
+        Compute loglikelihoods conditional on the current period's regime
+        """
+
+        # Get residuals
+        resid = self._resid(params)
+
+        # Compute the conditional likelihoods
+        variance = params[self.parameters['variance']].squeeze()
+        if self.switching_variance:
+            variance = np.reshape(variance, (self.k_regimes, 1, 1))
+
+        conditional_loglikelihoods = (
+            -0.5 * resid**2 / variance - 0.5 * np.log(2 * np.pi * variance))
+
+        return conditional_loglikelihoods
+
+    @property
+    def _res_classes(self):
+        return {'fit': (MarkovRegressionResults,
+                        MarkovRegressionResultsWrapper)}
+
+    def _em_iteration(self, params0):
+        """
+        EM iteration
+
+        Notes
+        -----
+        This uses the inherited _em_iteration method for computing the
+        non-TVTP transition probabilities and then performs the EM step for
+        regression coefficients and variances.
+        """
+        # Inherited parameters
+        result, params1 = super()._em_iteration(params0)
+
+        tmp = np.sqrt(result.smoothed_marginal_probabilities)
+
+        # Regression coefficients
+        coeffs = None
+        if self._k_exog > 0:
+            coeffs = self._em_exog(result, self.endog, self.exog,
+                                   self.parameters.switching['exog'], tmp)
+            for i in range(self.k_regimes):
+                params1[self.parameters[i, 'exog']] = coeffs[i]
+
+        # Variances
+        params1[self.parameters['variance']] = self._em_variance(
+            result, self.endog, self.exog, coeffs, tmp)
+        # params1[self.parameters['variance']] = 0.33282116
+
+        return result, params1
+
+    def _em_exog(self, result, endog, exog, switching, tmp=None):
+        """
+        EM step for regression coefficients
+        """
+        k_exog = exog.shape[1]
+        coeffs = np.zeros((self.k_regimes, k_exog))
+
+        # First, estimate non-switching coefficients
+        if not np.all(switching):
+            nonswitching_exog = exog[:, ~switching]
+            nonswitching_coeffs = (
+                np.dot(np.linalg.pinv(nonswitching_exog), endog))
+            coeffs[:, ~switching] = nonswitching_coeffs
+            endog = endog - np.dot(nonswitching_exog, nonswitching_coeffs)
+
+        # Next, get switching coefficients
+        if np.any(switching):
+            switching_exog = exog[:, switching]
+            if tmp is None:
+                tmp = np.sqrt(result.smoothed_marginal_probabilities)
+            for i in range(self.k_regimes):
+                tmp_endog = tmp[i] * endog
+                tmp_exog = tmp[i][:, np.newaxis] * switching_exog
+                coeffs[i, switching] = (
+                    np.dot(np.linalg.pinv(tmp_exog), tmp_endog))
+
+        return coeffs
+
+    def _em_variance(self, result, endog, exog, betas, tmp=None):
+        """
+        EM step for variances
+        """
+        k_exog = 0 if exog is None else exog.shape[1]
+
+        if self.switching_variance:
+            variance = np.zeros(self.k_regimes)
+            for i in range(self.k_regimes):
+                if k_exog > 0:
+                    resid = endog - np.dot(exog, betas[i])
+                else:
+                    resid = endog
+                variance[i] = (
+                    np.sum(resid**2 *
+                           result.smoothed_marginal_probabilities[i]) /
+                    np.sum(result.smoothed_marginal_probabilities[i]))
+        else:
+            variance = 0
+            if tmp is None:
+                tmp = np.sqrt(result.smoothed_marginal_probabilities)
+            for i in range(self.k_regimes):
+                tmp_endog = tmp[i] * endog
+                if k_exog > 0:
+                    tmp_exog = tmp[i][:, np.newaxis] * exog
+                    resid = tmp_endog - np.dot(tmp_exog, betas[i])
+                else:
+                    resid = tmp_endog
+                variance += np.sum(resid**2)
+            variance /= self.nobs
+        return variance
+
+    @property
+    def start_params(self):
+        """
+        (array) Starting parameters for maximum likelihood estimation.
+
+        Notes
+        -----
+        These are not very sophisticated and / or good. We set equal transition
+        probabilities and interpolate regression coefficients between zero and
+        the OLS estimates, where the interpolation is based on the regime
+        number. We rely heavily on the EM algorithm to quickly find much better
+        starting parameters, which are then used by the typical scoring
+        approach.
+        """
+        # Inherited parameters
+        params = markov_switching.MarkovSwitching.start_params.fget(self)
+
+        # Regression coefficients
+        if self._k_exog > 0:
+            beta = np.dot(np.linalg.pinv(self.exog), self.endog)
+            variance = np.var(self.endog - np.dot(self.exog, beta))
+
+            if np.any(self.switching_coeffs):
+                for i in range(self.k_regimes):
+                    params[self.parameters[i, 'exog']] = (
+                        beta * (i / self.k_regimes))
+            else:
+                params[self.parameters['exog']] = beta
+        else:
+            variance = np.var(self.endog)
+
+        # Variances
+        if self.switching_variance:
+            params[self.parameters['variance']] = (
+                np.linspace(variance / 10., variance, num=self.k_regimes))
+        else:
+            params[self.parameters['variance']] = variance
+
+        return params
+
+    @property
+    def param_names(self):
+        """
+        (list of str) List of human readable parameter names (for parameters
+        actually included in the model).
+        """
+        # Inherited parameters
+        param_names = np.array(
+            markov_switching.MarkovSwitching.param_names.fget(self),
+            dtype=object)
+
+        # Regression coefficients
+        if np.any(self.switching_coeffs):
+            for i in range(self.k_regimes):
+                param_names[self.parameters[i, 'exog']] = [
+                    '%s[%d]' % (exog_name, i) for exog_name in self.exog_names]
+        else:
+            param_names[self.parameters['exog']] = self.exog_names
+
+        # Variances
+        if self.switching_variance:
+            for i in range(self.k_regimes):
+                param_names[self.parameters[i, 'variance']] = 'sigma2[%d]' % i
+        else:
+            param_names[self.parameters['variance']] = 'sigma2'
+
+        return param_names.tolist()
+
+    def transform_params(self, unconstrained):
+        """
+        Transform unconstrained parameters used by the optimizer to constrained
+        parameters used in likelihood evaluation
+
+        Parameters
+        ----------
+        unconstrained : array_like
+            Array of unconstrained parameters used by the optimizer, to be
+            transformed.
+
+        Returns
+        -------
+        constrained : array_like
+            Array of constrained parameters which may be used in likelihood
+            evaluation.
+        """
+        # Inherited parameters
+        constrained = super().transform_params(
+            unconstrained)
+
+        # Nothing to do for regression coefficients
+        constrained[self.parameters['exog']] = (
+            unconstrained[self.parameters['exog']])
+
+        # Force variances to be positive
+        constrained[self.parameters['variance']] = (
+            unconstrained[self.parameters['variance']]**2)
+
+        return constrained
+
+    def untransform_params(self, constrained):
+        """
+        Transform constrained parameters used in likelihood evaluation
+        to unconstrained parameters used by the optimizer
+
+        Parameters
+        ----------
+        constrained : array_like
+            Array of constrained parameters used in likelihood evaluation, to
+            be transformed.
+
+        Returns
+        -------
+        unconstrained : array_like
+            Array of unconstrained parameters used by the optimizer.
+        """
+        # Inherited parameters
+        unconstrained = super().untransform_params(
+            constrained)
+
+        # Nothing to do for regression coefficients
+        unconstrained[self.parameters['exog']] = (
+            constrained[self.parameters['exog']])
+
+        # Force variances to be positive
+        unconstrained[self.parameters['variance']] = (
+            constrained[self.parameters['variance']]**0.5)
+
+        return unconstrained
+
+
+class MarkovRegressionResults(markov_switching.MarkovSwitchingResults):
+    r"""
+    Class to hold results from fitting a Markov switching regression model
+
+    Parameters
+    ----------
+    model : MarkovRegression instance
+        The fitted model instance
+    params : ndarray
+        Fitted parameters
+    filter_results : HamiltonFilterResults or KimSmootherResults instance
+        The underlying filter and, optionally, smoother output
+    cov_type : str
+        The type of covariance matrix estimator to use. Can be one of 'approx',
+        'opg', 'robust', or 'none'.
+
+    Attributes
+    ----------
+    model : Model instance
+        A reference to the model that was fit.
+    filter_results : HamiltonFilterResults or KimSmootherResults instance
+        The underlying filter and, optionally, smoother output
+    nobs : float
+        The number of observations used to fit the model.
+    params : ndarray
+        The parameters of the model.
+    scale : float
+        This is currently set to 1.0 and not used by the model or its results.
+    """
+    pass
+
+
+class MarkovRegressionResultsWrapper(
+        markov_switching.MarkovSwitchingResultsWrapper):
+    pass
+wrap.populate_wrapper(MarkovRegressionResultsWrapper,  # noqa:E305
+                      MarkovRegressionResults)

venv/lib/python3.11/site-packages/statsmodels/tsa/regime_switching/tests/results/results_predict_fedfunds.csv

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venv/lib/python3.11/site-packages/statsmodels/tsa/regime_switching/tests/test_markov_autoregression.py

@@ -0,0 +1,905 @@
+"""
+Tests for Markov Autoregression models
+
+Author: Chad Fulton
+License: BSD-3
+"""
+
+import warnings
+import os
+
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+import pandas as pd
+import pytest
+
+from statsmodels.tools import add_constant
+from statsmodels.tsa.regime_switching import markov_autoregression
+
+current_path = os.path.dirname(os.path.abspath(__file__))
+
+
+rgnp = [2.59316421, 2.20217133, 0.45827562, 0.9687438,
+        -0.24130757, 0.89647478, 2.05393219, 1.73353648,
+        0.93871289, -0.46477833, -0.80983406, -1.39763689,
+        -0.39886093, 1.1918416, 1.45620048, 2.11808228,
+        1.08957863, 1.32390273, 0.87296367, -0.19773273,
+        0.45420215, 0.07221876, 1.1030364, 0.82097489,
+        -0.05795795, 0.58447772, -1.56192672, -2.05041027,
+        0.53637183, 2.33676839, 2.34014559, 1.2339263,
+        1.8869648, -0.45920792, 0.84940469, 1.70139849,
+        -0.28756312, 0.09594627, -0.86080289, 1.03447127,
+        1.23685944, 1.42004502, 2.22410631, 1.30210173,
+        1.03517699, 0.9253425, -0.16559951, 1.3444382,
+        1.37500131, 1.73222184, 0.71605635, 2.21032143,
+        0.85333031, 1.00238776, 0.42725441, 2.14368343,
+        1.43789184, 1.57959926, 2.27469826, 1.95962656,
+        0.25992399, 1.01946914, 0.49016398, 0.5636338,
+        0.5959546, 1.43082857, 0.56230122, 1.15388393,
+        1.68722844, 0.77438205, -0.09647045, 1.39600146,
+        0.13646798, 0.55223715, -0.39944872, -0.61671102,
+        -0.08722561, 1.2101835, -0.90729755, 2.64916158,
+        -0.0080694, 0.51111895, -0.00401437, 2.16821432,
+        1.92586732, 1.03504717, 1.85897219, 2.32004929,
+        0.25570789, -0.09855274, 0.89073682, -0.55896485,
+        0.28350255, -1.31155407, -0.88278776, -1.97454941,
+        1.01275265, 1.68264723, 1.38271284, 1.86073637,
+        0.4447377, 0.41449001, 0.99202275, 1.36283576,
+        1.59970522, 1.98845816, -0.25684232, 0.87786949,
+        3.1095655, 0.85324478, 1.23337317, 0.00314302,
+        -0.09433369, 0.89883322, -0.19036628, 0.99772376,
+        -2.39120054, 0.06649673, 1.26136017, 1.91637838,
+        -0.3348029, 0.44207108, -1.40664911, -1.52129889,
+        0.29919869, -0.80197448, 0.15204792, 0.98585027,
+        2.13034606, 1.34397924, 1.61550522, 2.70930099,
+        1.24461412, 0.50835466, 0.14802167]
+
+rec = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+       0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0,
+       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
+       1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+       1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]
+
+
+def test_predict():
+    # AR(1) without mean, k_regimes=2
+    endog = np.ones(10)
+    markov_autoregression.MarkovAutoregression(
+        endog,
+        k_regimes=2,
+        order=1,
+        trend='n'
+    )
+    mod = markov_autoregression.MarkovAutoregression(
+        endog, k_regimes=2, order=1, trend='n')
+    assert_equal(mod.nobs, 9)
+    assert_equal(mod.endog, np.ones(9))
+
+    params = np.r_[0.5, 0.5, 1., 0.1, 0.5]
+    mod_resid = mod._resid(params)
+    resids = np.zeros((2, 2, mod.nobs))
+    # Resids when: S_{t} = 0
+    resids[0, :, :] = np.ones(9) - 0.1 * np.ones(9)
+    assert_allclose(mod_resid[0, :, :], resids[0, :, :])
+    # Resids when: S_{t} = 1
+    resids[1, :, :] = np.ones(9) - 0.5 * np.ones(9)
+    assert_allclose(mod_resid[1, :, :], resids[1, :, :])
+
+    # AR(1) with mean, k_regimes=2
+    endog = np.arange(10)
+    mod = markov_autoregression.MarkovAutoregression(
+        endog, k_regimes=2, order=1)
+    assert_equal(mod.nobs, 9)
+    assert_equal(mod.endog, np.arange(1, 10))
+
+    params = np.r_[0.5, 0.5, 2., 3., 1., 0.1, 0.5]
+    mod_resid = mod._resid(params)
+    resids = np.zeros((2, 2, mod.nobs))
+    # Resids when: S_t = 0, S_{t-1} = 0
+    resids[0, 0, :] = (np.arange(1, 10) - 2.) - 0.1 * (np.arange(9) - 2.)
+    assert_allclose(mod_resid[0, 0, :], resids[0, 0, :])
+    # Resids when: S_t = 0, S_{t-1} = 1
+    resids[0, 1, :] = (np.arange(1, 10) - 2.) - 0.1 * (np.arange(9) - 3.)
+    assert_allclose(mod_resid[0, 1, :], resids[0, 1, :])
+    # Resids when: S_t = 1, S_{t-1} = 0
+    resids[1, 0, :] = (np.arange(1, 10) - 3.) - 0.5 * (np.arange(9) - 2.)
+    assert_allclose(mod_resid[1, 0, :], resids[1, 0, :])
+    # Resids when: S_t = 1, S_{t-1} = 1
+    resids[1, 1, :] = (np.arange(1, 10) - 3.) - 0.5 * (np.arange(9) - 3.)
+    assert_allclose(mod_resid[1, 1, :], resids[1, 1, :])
+
+    # AR(2) with mean, k_regimes=3
+    endog = np.arange(10)
+    mod = markov_autoregression.MarkovAutoregression(
+        endog, k_regimes=3, order=2)
+    assert_equal(mod.nobs, 8)
+    assert_equal(mod.endog, np.arange(2, 10))
+
+    params = np.r_[[0.3] * 6, 2., 3., 4, 1., 0.1, 0.5, 0.8, -0.05, -0.25, -0.4]
+    mod_resid = mod._resid(params)
+    resids = np.zeros((3, 3, 3, mod.nobs))
+    # Resids when: S_t = 0, S_{t-1} = 0, S_{t-2} = 0
+    resids[0, 0, 0, :] = (
+        (np.arange(2, 10) - 2.) -
+        0.1 * (np.arange(1, 9) - 2.) -
+        (-0.05) * (np.arange(8) - 2.))
+    assert_allclose(mod_resid[0, 0, 0, :], resids[0, 0, 0, :])
+
+    # Resids when: S_t = 1, S_{t-1} = 0, S_{t-2} = 0
+    resids[1, 0, 0, :] = (
+        (np.arange(2, 10) - 3.) -
+        0.5 * (np.arange(1, 9) - 2.) -
+        (-0.25) * (np.arange(8) - 2.))
+    assert_allclose(mod_resid[1, 0, 0, :], resids[1, 0, 0, :])
+
+    # Resids when: S_t = 0, S_{t-1} = 2, S_{t-2} = 1
+    resids[0, 2, 1, :] = (
+        (np.arange(2, 10) - 2.) -
+        0.1 * (np.arange(1, 9) - 4.) -
+        (-0.05) * (np.arange(8) - 3.))
+    assert_allclose(mod_resid[0, 2, 1, :], resids[0, 2, 1, :])
+
+    # AR(1) with mean + non-switching exog
+    endog = np.arange(10)
+    exog = np.r_[0.4, 5, 0.2, 1.2, -0.3, 2.5, 0.2, -0.7, 2., -1.1]
+    mod = markov_autoregression.MarkovAutoregression(
+        endog, k_regimes=2, order=1, exog=exog)
+    assert_equal(mod.nobs, 9)
+    assert_equal(mod.endog, np.arange(1, 10))
+
+    params = np.r_[0.5, 0.5, 2., 3., 1.5, 1., 0.1, 0.5]
+    mod_resid = mod._resid(params)
+    resids = np.zeros((2, 2, mod.nobs))
+    # Resids when: S_t = 0, S_{t-1} = 0
+    resids[0, 0, :] = (
+        (np.arange(1, 10) - 2. - 1.5 * exog[1:]) -
+        0.1 * (np.arange(9) - 2. - 1.5 * exog[:-1]))
+    assert_allclose(mod_resid[0, 0, :], resids[0, 0, :])
+    # Resids when: S_t = 0, S_{t-1} = 1
+    resids[0, 1, :] = (
+        (np.arange(1, 10) - 2. - 1.5 * exog[1:]) -
+        0.1 * (np.arange(9) - 3. - 1.5 * exog[:-1]))
+    assert_allclose(mod_resid[0, 1, :], resids[0, 1, :])
+    # Resids when: S_t = 1, S_{t-1} = 0
+    resids[1, 0, :] = (
+        (np.arange(1, 10) - 3. - 1.5 * exog[1:]) -
+        0.5 * (np.arange(9) - 2. - 1.5 * exog[:-1]))
+    assert_allclose(mod_resid[1, 0, :], resids[1, 0, :])
+    # Resids when: S_t = 1, S_{t-1} = 1
+    resids[1, 1, :] = (
+        (np.arange(1, 10) - 3. - 1.5 * exog[1:]) -
+        0.5 * (np.arange(9) - 3. - 1.5 * exog[:-1]))
+    assert_allclose(mod_resid[1, 1, :], resids[1, 1, :])
+
+
+def test_conditional_loglikelihoods():
+    # AR(1) without mean, k_regimes=2, non-switching variance
+    endog = np.ones(10)
+    mod = markov_autoregression.MarkovAutoregression(
+        endog, k_regimes=2, order=1)
+    assert_equal(mod.nobs, 9)
+    assert_equal(mod.endog, np.ones(9))
+
+    params = np.r_[0.5, 0.5, 2., 3., 2., 0.1, 0.5]
+    resid = mod._resid(params)
+    conditional_likelihoods = (
+        np.exp(-0.5 * resid**2 / 2) / np.sqrt(2 * np.pi * 2))
+    assert_allclose(mod._conditional_loglikelihoods(params),
+                    np.log(conditional_likelihoods))
+
+    # AR(1) without mean, k_regimes=3, switching variance
+    endog = np.ones(10)
+    mod = markov_autoregression.MarkovAutoregression(
+        endog, k_regimes=3, order=1, switching_variance=True)
+    assert_equal(mod.nobs, 9)
+    assert_equal(mod.endog, np.ones(9))
+
+    params = np.r_[[0.3]*6, 2., 3., 4., 1.5, 3., 4.5, 0.1, 0.5, 0.8]
+    mod_conditional_loglikelihoods = mod._conditional_loglikelihoods(params)
+    conditional_likelihoods = mod._resid(params)
+
+    # S_t = 0
+    conditional_likelihoods[0, :, :] = (
+        np.exp(-0.5 * conditional_likelihoods[0, :, :]**2 / 1.5) /
+        np.sqrt(2 * np.pi * 1.5))
+    assert_allclose(mod_conditional_loglikelihoods[0, :, :],
+                    np.log(conditional_likelihoods[0, :, :]))
+    # S_t = 1
+    conditional_likelihoods[1, :, :] = (
+        np.exp(-0.5 * conditional_likelihoods[1, :, :]**2 / 3.) /
+        np.sqrt(2 * np.pi * 3.))
+    assert_allclose(mod_conditional_loglikelihoods[1, :, :],
+                    np.log(conditional_likelihoods[1, :, :]))
+    # S_t = 2
+    conditional_likelihoods[2, :, :] = (
+        np.exp(-0.5 * conditional_likelihoods[2, :, :]**2 / 4.5) /
+        np.sqrt(2 * np.pi * 4.5))
+    assert_allclose(mod_conditional_loglikelihoods[2, :, :],
+                    np.log(conditional_likelihoods[2, :, :]))
+
+
+class MarkovAutoregression:
+    @classmethod
+    def setup_class(cls, true, endog, atol=1e-5, rtol=1e-7, **kwargs):
+        cls.model = markov_autoregression.MarkovAutoregression(endog, **kwargs)
+        cls.true = true
+        cls.result = cls.model.smooth(cls.true['params'])
+        cls.atol = atol
+        cls.rtol = rtol
+
+    def test_llf(self):
+        assert_allclose(self.result.llf, self.true['llf'], atol=self.atol,
+                        rtol=self.rtol)
+
+    def test_fit(self, **kwargs):
+        # Test fitting against Stata
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            res = self.model.fit(disp=False, **kwargs)
+        assert_allclose(res.llf, self.true['llf_fit'], atol=self.atol,
+                        rtol=self.rtol)
+
+    @pytest.mark.smoke
+    def test_fit_em(self, **kwargs):
+        # Test EM fitting (smoke test)
+        res_em = self.model._fit_em(**kwargs)
+        assert_allclose(res_em.llf, self.true['llf_fit_em'], atol=self.atol,
+                        rtol=self.rtol)
+
+
+hamilton_ar2_short_filtered_joint_probabilities = np.array([
+         [[[4.99506987e-02,   6.44048275e-04,   6.22227140e-05,
+            4.45756755e-06,   5.26645567e-07,   7.99846146e-07,
+            1.19425705e-05,   6.87762063e-03],
+           [1.95930395e-02,   3.25884335e-04,   1.12955091e-04,
+            3.38537103e-04,   9.81927968e-06,   2.71696750e-05,
+            5.83828290e-03,   7.64261509e-02]],
+
+          [[1.97113193e-03,   9.50372207e-05,   1.98390978e-04,
+            1.88188953e-06,   4.83449400e-07,   1.14872860e-05,
+            4.02918239e-06,   4.35015431e-04],
+           [2.24870443e-02,   1.27331172e-03,   9.62155856e-03,
+            4.04178695e-03,   2.75516282e-04,   1.18179572e-02,
+            5.99778157e-02,   1.48149567e-01]]],
+
+
+         [[[6.70912859e-02,   1.84223872e-02,   2.55621792e-04,
+            4.48500688e-05,   7.80481515e-05,   2.73734559e-06,
+            7.59835896e-06,   1.42930726e-03],
+           [2.10053328e-02,   7.44036383e-03,   3.70388879e-04,
+            2.71878370e-03,   1.16152088e-03,   7.42182691e-05,
+            2.96490192e-03,   1.26774695e-02]],
+
+          [[8.09335679e-02,   8.31016518e-02,   2.49149080e-02,
+            5.78825626e-04,   2.19019941e-03,   1.20179130e-03,
+            7.83659430e-05,   2.76363377e-03],
+           [7.36967899e-01,   8.88697316e-01,   9.64463954e-01,
+            9.92270877e-01,   9.96283886e-01,   9.86863839e-01,
+            9.31117063e-01,   7.51241236e-01]]]])
+
+
+hamilton_ar2_short_predicted_joint_probabilities = np.array([[
+          [[[1.20809334e-01,   3.76964436e-02,   4.86045844e-04,
+             4.69578023e-05,   3.36400588e-06,   3.97445190e-07,
+             6.03622290e-07,   9.01273552e-06],
+            [3.92723623e-02,   1.47863379e-02,   2.45936108e-04,
+             8.52441571e-05,   2.55484811e-04,   7.41034525e-06,
+             2.05042201e-05,   4.40599447e-03]],
+
+           [[4.99131230e-03,   1.48756005e-03,   7.17220245e-05,
+             1.49720314e-04,   1.42021122e-06,   3.64846209e-07,
+             8.66914462e-06,   3.04071516e-06],
+            [4.70476003e-02,   1.69703652e-02,   9.60933974e-04,
+             7.26113047e-03,   3.05022748e-03,   2.07924699e-04,
+             8.91869322e-03,   4.52636381e-02]]],
+
+
+          [[[4.99131230e-03,   6.43506069e-03,   1.76698327e-03,
+             2.45179642e-05,   4.30179435e-06,   7.48598845e-06,
+             2.62552503e-07,   7.28796600e-07],
+            [1.62256192e-03,   2.01472650e-03,   7.13642497e-04,
+             3.55258493e-05,   2.60772139e-04,   1.11407276e-04,
+             7.11864528e-06,   2.84378568e-04]],
+
+           [[5.97950448e-03,   7.76274317e-03,   7.97069493e-03,
+             2.38971340e-03,   5.55180599e-05,   2.10072977e-04,
+             1.15269812e-04,   7.51646942e-06],
+            [5.63621989e-02,   7.06862760e-02,   8.52394030e-02,
+             9.25065601e-02,   9.51736612e-02,   9.55585689e-02,
+             9.46550451e-02,   8.93080931e-02]]]],
+
+
+
+         [[[[3.92723623e-02,   1.22542551e-02,   1.58002431e-04,
+             1.52649118e-05,   1.09356167e-06,   1.29200377e-07,
+             1.96223855e-07,   2.92983500e-06],
+            [1.27665503e-02,   4.80670161e-03,   7.99482261e-05,
+             2.77109335e-05,   8.30522919e-05,   2.40893443e-06,
+             6.66545485e-06,   1.43228843e-03]],
+
+           [[1.62256192e-03,   4.83571884e-04,   2.33151963e-05,
+             4.86706634e-05,   4.61678312e-07,   1.18603191e-07,
+             2.81814142e-06,   9.88467229e-07],
+            [1.52941031e-02,   5.51667911e-03,   3.12377744e-04,
+             2.36042810e-03,   9.91559466e-04,   6.75915830e-05,
+             2.89926399e-03,   1.47141776e-02]]],
+
+
+          [[[4.70476003e-02,   6.06562252e-02,   1.66554040e-02,
+             2.31103828e-04,   4.05482745e-05,   7.05621631e-05,
+             2.47479309e-06,   6.86956236e-06],
+            [1.52941031e-02,   1.89906063e-02,   6.72672133e-03,
+             3.34863029e-04,   2.45801156e-03,   1.05011361e-03,
+             6.70996238e-05,   2.68052335e-03]],
+
+           [[5.63621989e-02,   7.31708248e-02,   7.51309569e-02,
+             2.25251946e-02,   5.23307566e-04,   1.98012644e-03,
+             1.08652148e-03,   7.08494735e-05],
+            [5.31264334e-01,   6.66281623e-01,   8.03457913e-01,
+             8.71957394e-01,   8.97097216e-01,   9.00725317e-01,
+             8.92208794e-01,   8.41808970e-01]]]]])
+
+
+hamilton_ar2_short_smoothed_joint_probabilities = np.array([
+         [[[1.29898189e-02,   1.66298475e-04,   1.29822987e-05,
+            9.95268382e-07,   1.84473346e-07,   7.18761267e-07,
+            1.69576494e-05,   6.87762063e-03],
+           [5.09522472e-03,   8.41459714e-05,   2.35672254e-05,
+            7.55872505e-05,   3.43949612e-06,   2.44153330e-05,
+            8.28997024e-03,   7.64261509e-02]],
+
+          [[5.90021731e-04,   2.55342733e-05,   4.50698224e-05,
+            5.30734135e-07,   1.80741761e-07,   1.11483792e-05,
+            5.98539007e-06,   4.35015431e-04],
+           [6.73107901e-03,   3.42109009e-04,   2.18579464e-03,
+            1.13987259e-03,   1.03004157e-04,   1.14692946e-02,
+            8.90976350e-02,   1.48149567e-01]]],
+
+
+         [[[6.34648123e-02,   1.79187451e-02,   2.37462147e-04,
+            3.55542558e-05,   7.63980455e-05,   2.90520820e-06,
+            8.17644492e-06,   1.42930726e-03],
+           [1.98699352e-02,   7.23695477e-03,   3.44076057e-04,
+            2.15527721e-03,   1.13696383e-03,   7.87695658e-05,
+            3.19047276e-03,   1.26774695e-02]],
+
+          [[8.81925054e-02,   8.33092133e-02,   2.51106301e-02,
+            5.81007470e-04,   2.19065072e-03,   1.20221350e-03,
+            7.56893839e-05,   2.76363377e-03],
+           [8.03066603e-01,   8.90916999e-01,   9.72040418e-01,
+            9.96011175e-01,   9.96489179e-01,   9.87210535e-01,
+            8.99315113e-01,   7.51241236e-01]]]])
+
+
+class TestHamiltonAR2Short(MarkovAutoregression):
+    # This is just a set of regression tests
+    @classmethod
+    def setup_class(cls):
+        true = {
+            'params': np.r_[0.754673, 0.095915, -0.358811, 1.163516,
+                            np.exp(-0.262658)**2, 0.013486, -0.057521],
+            'llf': -10.14066,
+            'llf_fit': -4.0523073,
+            'llf_fit_em': -8.885836
+        }
+        super().setup_class(
+            true, rgnp[-10:], k_regimes=2, order=2, switching_ar=False)
+
+    def test_fit_em(self):
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            super().test_fit_em()
+
+    def test_filter_output(self, **kwargs):
+        res = self.result
+
+        # Filtered
+        assert_allclose(res.filtered_joint_probabilities,
+                        hamilton_ar2_short_filtered_joint_probabilities)
+
+        # Predicted
+        desired = hamilton_ar2_short_predicted_joint_probabilities
+        if desired.ndim > res.predicted_joint_probabilities.ndim:
+            desired = desired.sum(axis=-2)
+        assert_allclose(res.predicted_joint_probabilities, desired)
+
+    def test_smoother_output(self, **kwargs):
+        res = self.result
+
+        # Filtered
+        assert_allclose(res.filtered_joint_probabilities,
+                        hamilton_ar2_short_filtered_joint_probabilities)
+
+        # Predicted
+        desired = hamilton_ar2_short_predicted_joint_probabilities
+        if desired.ndim > res.predicted_joint_probabilities.ndim:
+            desired = desired.sum(axis=-2)
+        assert_allclose(res.predicted_joint_probabilities, desired)
+
+        # Smoothed, entry-by-entry
+        assert_allclose(
+            res.smoothed_joint_probabilities[..., -1],
+            hamilton_ar2_short_smoothed_joint_probabilities[..., -1])
+        assert_allclose(
+            res.smoothed_joint_probabilities[..., -2],
+            hamilton_ar2_short_smoothed_joint_probabilities[..., -2])
+        assert_allclose(
+            res.smoothed_joint_probabilities[..., -3],
+            hamilton_ar2_short_smoothed_joint_probabilities[..., -3])
+        assert_allclose(
+            res.smoothed_joint_probabilities[..., :-3],
+            hamilton_ar2_short_smoothed_joint_probabilities[..., :-3])
+
+
+hamilton_ar4_filtered = [
+    0.776712, 0.949192, 0.996320, 0.990258, 0.940111, 0.537442,
+    0.140001, 0.008942, 0.048480, 0.614097, 0.910889, 0.995463,
+    0.979465, 0.992324, 0.984561, 0.751038, 0.776268, 0.522048,
+    0.814956, 0.821786, 0.472729, 0.673567, 0.029031, 0.001556,
+    0.433276, 0.985463, 0.995025, 0.966067, 0.998445, 0.801467,
+    0.960997, 0.996431, 0.461365, 0.199357, 0.027398, 0.703626,
+    0.946388, 0.985321, 0.998244, 0.989567, 0.984510, 0.986811,
+    0.793788, 0.973675, 0.984848, 0.990418, 0.918427, 0.998769,
+    0.977647, 0.978742, 0.927635, 0.998691, 0.988934, 0.991654,
+    0.999288, 0.999073, 0.918636, 0.987710, 0.966876, 0.910015,
+    0.826150, 0.969451, 0.844049, 0.941525, 0.993363, 0.949978,
+    0.615206, 0.970915, 0.787585, 0.707818, 0.200476, 0.050835,
+    0.140723, 0.809850, 0.086422, 0.990344, 0.785963, 0.817425,
+    0.659152, 0.996578, 0.992860, 0.948501, 0.996883, 0.999712,
+    0.906694, 0.725013, 0.963690, 0.386960, 0.241302, 0.009078,
+    0.015789, 0.000896, 0.541530, 0.928686, 0.953704, 0.992741,
+    0.935877, 0.918958, 0.977316, 0.987941, 0.987300, 0.996769,
+    0.645469, 0.921285, 0.999917, 0.949335, 0.968914, 0.886025,
+    0.777141, 0.904381, 0.368277, 0.607429, 0.002491, 0.227610,
+    0.871284, 0.987717, 0.288705, 0.512124, 0.030329, 0.005177,
+    0.256183, 0.020955, 0.051620, 0.549009, 0.991715, 0.987892,
+    0.995377, 0.999833, 0.993756, 0.956164, 0.927714]
+
+hamilton_ar4_smoothed = [
+    0.968096, 0.991071, 0.998559, 0.958534, 0.540652, 0.072784,
+    0.010999, 0.006228, 0.172144, 0.898574, 0.989054, 0.998293,
+    0.986434, 0.993248, 0.976868, 0.858521, 0.847452, 0.675670,
+    0.596294, 0.165407, 0.035270, 0.127967, 0.007414, 0.004944,
+    0.815829, 0.998128, 0.998091, 0.993227, 0.999283, 0.921100,
+    0.977171, 0.971757, 0.124680, 0.063710, 0.114570, 0.954701,
+    0.994852, 0.997302, 0.999345, 0.995817, 0.996218, 0.994580,
+    0.933990, 0.996054, 0.998151, 0.996976, 0.971489, 0.999786,
+    0.997362, 0.996755, 0.993053, 0.999947, 0.998469, 0.997987,
+    0.999830, 0.999360, 0.953176, 0.992673, 0.975235, 0.938121,
+    0.946784, 0.986897, 0.905792, 0.969755, 0.995379, 0.914480,
+    0.772814, 0.931385, 0.541742, 0.394596, 0.063428, 0.027829,
+    0.124527, 0.286105, 0.069362, 0.995950, 0.961153, 0.962449,
+    0.945022, 0.999855, 0.998943, 0.980041, 0.999028, 0.999838,
+    0.863305, 0.607421, 0.575983, 0.013300, 0.007562, 0.000635,
+    0.001806, 0.002196, 0.803550, 0.972056, 0.984503, 0.998059,
+    0.985211, 0.988486, 0.994452, 0.994498, 0.998873, 0.999192,
+    0.870482, 0.976282, 0.999961, 0.984283, 0.973045, 0.786176,
+    0.403673, 0.275418, 0.115199, 0.257560, 0.004735, 0.493936,
+    0.907360, 0.873199, 0.052959, 0.076008, 0.001653, 0.000847,
+    0.062027, 0.021257, 0.219547, 0.955654, 0.999851, 0.997685,
+    0.998324, 0.999939, 0.996858, 0.969209, 0.927714]
+
+
+class TestHamiltonAR4(MarkovAutoregression):
+    @classmethod
+    def setup_class(cls):
+        # Results from E-views:
+        # Dependent variable followed by a list of switching regressors:
+        #     rgnp c
+        # List of non-switching regressors:
+        #     ar(1) ar(2) ar(3) ar(4)
+        # Do not check "Regime specific error variances"
+        # Switching type: Markov
+        # Number of Regimes: 2
+        # Probability regressors:
+        #     c
+        # Method SWITCHREG
+        # Sample 1951q1 1984q4
+        true = {
+            'params': np.r_[0.754673, 0.095915, -0.358811, 1.163516,
+                            np.exp(-0.262658)**2, 0.013486, -0.057521,
+                            -0.246983, -0.212923],
+            'llf': -181.26339,
+            'llf_fit': -181.26339,
+            'llf_fit_em': -183.85444,
+            'bse_oim': np.r_[.0965189, .0377362, .2645396, .0745187, np.nan,
+                             .1199942, .137663, .1069103, .1105311, ]
+        }
+        super().setup_class(
+            true, rgnp, k_regimes=2, order=4, switching_ar=False)
+
+    def test_filtered_regimes(self):
+        res = self.result
+        assert_equal(len(res.filtered_marginal_probabilities[:, 1]),
+                     self.model.nobs)
+        assert_allclose(res.filtered_marginal_probabilities[:, 1],
+                        hamilton_ar4_filtered, atol=1e-5)
+
+    def test_smoothed_regimes(self):
+        res = self.result
+        assert_equal(len(res.smoothed_marginal_probabilities[:, 1]),
+                     self.model.nobs)
+        assert_allclose(res.smoothed_marginal_probabilities[:, 1],
+                        hamilton_ar4_smoothed, atol=1e-5)
+
+    def test_bse(self):
+        # Cannot compare middle element of bse because we estimate sigma^2
+        # rather than sigma
+        bse = self.result.cov_params_approx.diagonal()**0.5
+        assert_allclose(bse[:4], self.true['bse_oim'][:4], atol=1e-6)
+        assert_allclose(bse[6:], self.true['bse_oim'][6:], atol=1e-6)
+
+
+class TestHamiltonAR2Switch(MarkovAutoregression):
+    # Results from Stata, see http://www.stata.com/manuals14/tsmswitch.pdf
+    @classmethod
+    def setup_class(cls):
+        path = os.path.join(current_path, 'results',
+                            'results_predict_rgnp.csv')
+        results = pd.read_csv(path)
+
+        true = {
+            'params': np.r_[.3812383, .3564492, -.0055216, 1.195482,
+                            .6677098**2, .3710719, .4621503, .7002937,
+                            -.3206652],
+            'llf': -179.32354,
+            'llf_fit': -179.38684,
+            'llf_fit_em': -184.99606,
+            'bse_oim': np.r_[.1424841, .0994742, .2057086, .1225987, np.nan,
+                             .1754383, .1652473, .187409, .1295937],
+            'smoothed0': results.iloc[3:]['switchar2_sm1'],
+            'smoothed1': results.iloc[3:]['switchar2_sm2'],
+            'predict0': results.iloc[3:]['switchar2_yhat1'],
+            'predict1': results.iloc[3:]['switchar2_yhat2'],
+            'predict_predicted': results.iloc[3:]['switchar2_pyhat'],
+            'predict_filtered': results.iloc[3:]['switchar2_fyhat'],
+            'predict_smoothed': results.iloc[3:]['switchar2_syhat'],
+        }
+        super().setup_class(
+            true, rgnp, k_regimes=2, order=2)
+
+    def test_smoothed_marginal_probabilities(self):
+        assert_allclose(self.result.smoothed_marginal_probabilities[:, 0],
+                        self.true['smoothed0'], atol=1e-6)
+        assert_allclose(self.result.smoothed_marginal_probabilities[:, 1],
+                        self.true['smoothed1'], atol=1e-6)
+
+    def test_predict(self):
+        # Smoothed
+        actual = self.model.predict(
+            self.true['params'], probabilities='smoothed')
+        assert_allclose(actual, self.true['predict_smoothed'], atol=1e-6)
+        actual = self.model.predict(
+            self.true['params'], probabilities=None)
+        assert_allclose(actual, self.true['predict_smoothed'], atol=1e-6)
+
+        actual = self.result.predict(probabilities='smoothed')
+        assert_allclose(actual, self.true['predict_smoothed'], atol=1e-6)
+        actual = self.result.predict(probabilities=None)
+        assert_allclose(actual, self.true['predict_smoothed'], atol=1e-6)
+
+    def test_bse(self):
+        # Cannot compare middle element of bse because we estimate sigma^2
+        # rather than sigma
+        bse = self.result.cov_params_approx.diagonal()**0.5
+        assert_allclose(bse[:4], self.true['bse_oim'][:4], atol=1e-7)
+        assert_allclose(bse[6:], self.true['bse_oim'][6:], atol=1e-7)
+
+
+hamilton_ar1_switch_filtered = [
+    0.840288, 0.730337, 0.900234, 0.596492, 0.921618, 0.983828,
+    0.959039, 0.898366, 0.477335, 0.251089, 0.049367, 0.386782,
+    0.942868, 0.965632, 0.982857, 0.897603, 0.946986, 0.916413,
+    0.640912, 0.849296, 0.778371, 0.954420, 0.929906, 0.723930,
+    0.891196, 0.061163, 0.004806, 0.977369, 0.997871, 0.977950,
+    0.896580, 0.963246, 0.430539, 0.906586, 0.974589, 0.514506,
+    0.683457, 0.276571, 0.956475, 0.966993, 0.971618, 0.987019,
+    0.916670, 0.921652, 0.930265, 0.655554, 0.965858, 0.964981,
+    0.976790, 0.868267, 0.983240, 0.852052, 0.919150, 0.854467,
+    0.987868, 0.935840, 0.958138, 0.979535, 0.956541, 0.716322,
+    0.919035, 0.866437, 0.899609, 0.914667, 0.976448, 0.867252,
+    0.953075, 0.977850, 0.884242, 0.688299, 0.968461, 0.737517,
+    0.870674, 0.559413, 0.380339, 0.582813, 0.941311, 0.240020,
+    0.999349, 0.619258, 0.828343, 0.729726, 0.991009, 0.966291,
+    0.899148, 0.970798, 0.977684, 0.695877, 0.637555, 0.915824,
+    0.434600, 0.771277, 0.113756, 0.144002, 0.008466, 0.994860,
+    0.993173, 0.961722, 0.978555, 0.789225, 0.836283, 0.940383,
+    0.968368, 0.974473, 0.980248, 0.518125, 0.904086, 0.993023,
+    0.802936, 0.920906, 0.685445, 0.666524, 0.923285, 0.643861,
+    0.938184, 0.008862, 0.945406, 0.990061, 0.991500, 0.486669,
+    0.805039, 0.089036, 0.025067, 0.863309, 0.352784, 0.733295,
+    0.928710, 0.984257, 0.926597, 0.959887, 0.984051, 0.872682,
+    0.824375, 0.780157]
+
+hamilton_ar1_switch_smoothed = [
+    0.900074, 0.758232, 0.914068, 0.637248, 0.901951, 0.979905,
+    0.958935, 0.888641, 0.261602, 0.148761, 0.056919, 0.424396,
+    0.932184, 0.954962, 0.983958, 0.895595, 0.949519, 0.923473,
+    0.678898, 0.848793, 0.807294, 0.958868, 0.942936, 0.809137,
+    0.960892, 0.032947, 0.007127, 0.967967, 0.996551, 0.979278,
+    0.896181, 0.987462, 0.498965, 0.908803, 0.986893, 0.488720,
+    0.640492, 0.325552, 0.951996, 0.959703, 0.960914, 0.986989,
+    0.916779, 0.924570, 0.935348, 0.677118, 0.960749, 0.958966,
+    0.976974, 0.838045, 0.986562, 0.847774, 0.908866, 0.821110,
+    0.984965, 0.915302, 0.938196, 0.976518, 0.973780, 0.744159,
+    0.922006, 0.873292, 0.904035, 0.917547, 0.978559, 0.870915,
+    0.948420, 0.979747, 0.884791, 0.711085, 0.973235, 0.726311,
+    0.828305, 0.446642, 0.411135, 0.639357, 0.973151, 0.141707,
+    0.999805, 0.618207, 0.783239, 0.672193, 0.987618, 0.964655,
+    0.877390, 0.962437, 0.989002, 0.692689, 0.699370, 0.937934,
+    0.522535, 0.824567, 0.058746, 0.146549, 0.009864, 0.994072,
+    0.992084, 0.956945, 0.984297, 0.795926, 0.845698, 0.935364,
+    0.963285, 0.972767, 0.992168, 0.528278, 0.826349, 0.996574,
+    0.811431, 0.930873, 0.680756, 0.721072, 0.937977, 0.731879,
+    0.996745, 0.016121, 0.951187, 0.989820, 0.996968, 0.592477,
+    0.889144, 0.036015, 0.040084, 0.858128, 0.418984, 0.746265,
+    0.907990, 0.980984, 0.900449, 0.934741, 0.986807, 0.872818,
+    0.812080, 0.780157]
+
+
+class TestHamiltonAR1Switch(MarkovAutoregression):
+    @classmethod
+    def setup_class(cls):
+        # Results from E-views:
+        # Dependent variable followed by a list of switching regressors:
+        #     rgnp c ar(1)
+        # List of non-switching regressors: <blank>
+        # Do not check "Regime specific error variances"
+        # Switching type: Markov
+        # Number of Regimes: 2
+        # Probability regressors:
+        #     c
+        # Method SWITCHREG
+        # Sample 1951q1 1984q4
+        true = {
+            'params': np.r_[0.85472458, 0.53662099, 1.041419, -0.479157,
+                            np.exp(-0.231404)**2, 0.243128, 0.713029],
+            'llf': -186.7575,
+            'llf_fit': -186.7575,
+            'llf_fit_em': -189.25446
+        }
+        super().setup_class(
+            true, rgnp, k_regimes=2, order=1)
+
+    def test_filtered_regimes(self):
+        assert_allclose(self.result.filtered_marginal_probabilities[:, 0],
+                        hamilton_ar1_switch_filtered, atol=1e-5)
+
+    def test_smoothed_regimes(self):
+        assert_allclose(self.result.smoothed_marginal_probabilities[:, 0],
+                        hamilton_ar1_switch_smoothed, atol=1e-5)
+
+    def test_expected_durations(self):
+        expected_durations = [6.883477, 1.863513]
+        assert_allclose(self.result.expected_durations, expected_durations,
+                        atol=1e-5)
+
+
+hamilton_ar1_switch_tvtp_filtered = [
+    0.999996, 0.999211, 0.999849, 0.996007, 0.999825, 0.999991,
+    0.999981, 0.999819, 0.041745, 0.001116, 1.74e-05, 0.000155,
+    0.999976, 0.999958, 0.999993, 0.999878, 0.999940, 0.999791,
+    0.996553, 0.999486, 0.998485, 0.999894, 0.999765, 0.997657,
+    0.999619, 0.002853, 1.09e-05, 0.999884, 0.999996, 0.999997,
+    0.999919, 0.999987, 0.989762, 0.999807, 0.999978, 0.050734,
+    0.010660, 0.000217, 0.006174, 0.999977, 0.999954, 0.999995,
+    0.999934, 0.999867, 0.999824, 0.996783, 0.999941, 0.999948,
+    0.999981, 0.999658, 0.999994, 0.999753, 0.999859, 0.999330,
+    0.999993, 0.999956, 0.999970, 0.999996, 0.999991, 0.998674,
+    0.999869, 0.999432, 0.999570, 0.999600, 0.999954, 0.999499,
+    0.999906, 0.999978, 0.999712, 0.997441, 0.999948, 0.998379,
+    0.999578, 0.994745, 0.045936, 0.006816, 0.027384, 0.000278,
+    1.000000, 0.996382, 0.999541, 0.998130, 0.999992, 0.999990,
+    0.999860, 0.999986, 0.999997, 0.998520, 0.997777, 0.999821,
+    0.033353, 0.011629, 6.95e-05, 4.52e-05, 2.04e-06, 0.999963,
+    0.999977, 0.999949, 0.999986, 0.999240, 0.999373, 0.999858,
+    0.999946, 0.999972, 0.999991, 0.994039, 0.999817, 0.999999,
+    0.999715, 0.999924, 0.997763, 0.997944, 0.999825, 0.996592,
+    0.695147, 0.000161, 0.999665, 0.999928, 0.999988, 0.992742,
+    0.374214, 0.001569, 2.16e-05, 0.000941, 4.32e-05, 0.000556,
+    0.999955, 0.999993, 0.999942, 0.999973, 0.999999, 0.999919,
+    0.999438, 0.998738]
+
+hamilton_ar1_switch_tvtp_smoothed = [
+    0.999997, 0.999246, 0.999918, 0.996118, 0.999740, 0.999990,
+    0.999984, 0.999783, 0.035454, 0.000958, 1.53e-05, 0.000139,
+    0.999973, 0.999939, 0.999994, 0.999870, 0.999948, 0.999884,
+    0.997243, 0.999668, 0.998424, 0.999909, 0.999860, 0.998037,
+    0.999559, 0.002533, 1.16e-05, 0.999801, 0.999993, 0.999997,
+    0.999891, 0.999994, 0.990096, 0.999753, 0.999974, 0.048495,
+    0.009289, 0.000542, 0.005991, 0.999974, 0.999929, 0.999995,
+    0.999939, 0.999880, 0.999901, 0.996221, 0.999937, 0.999935,
+    0.999985, 0.999450, 0.999995, 0.999768, 0.999897, 0.998930,
+    0.999992, 0.999949, 0.999954, 0.999995, 0.999994, 0.998687,
+    0.999902, 0.999547, 0.999653, 0.999538, 0.999966, 0.999485,
+    0.999883, 0.999982, 0.999831, 0.996940, 0.999968, 0.998678,
+    0.999780, 0.993895, 0.055372, 0.020421, 0.022913, 0.000127,
+    1.000000, 0.997072, 0.999715, 0.996893, 0.999990, 0.999991,
+    0.999811, 0.999978, 0.999998, 0.999100, 0.997866, 0.999787,
+    0.034912, 0.009932, 5.91e-05, 3.99e-05, 1.77e-06, 0.999954,
+    0.999976, 0.999932, 0.999991, 0.999429, 0.999393, 0.999845,
+    0.999936, 0.999961, 0.999995, 0.994246, 0.999570, 1.000000,
+    0.999702, 0.999955, 0.998611, 0.998019, 0.999902, 0.998486,
+    0.673991, 0.000205, 0.999627, 0.999902, 0.999994, 0.993707,
+    0.338707, 0.001359, 2.36e-05, 0.000792, 4.47e-05, 0.000565,
+    0.999932, 0.999993, 0.999931, 0.999950, 0.999999, 0.999940,
+    0.999626, 0.998738]
+
+expected_durations = [
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [1.223309, 1864.084],
+    [1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [1.223309, 1864.084], [1.223309, 1864.084],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [1.223309, 1864.084],
+    [1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [1.223309, 1864.084],
+    [1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084],
+    [1.223309, 1864.084], [1.223309, 1864.084], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [1.223309, 1864.084], [1.223309, 1864.084], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084],
+    [1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
+    [710.7573, 1.000391], [710.7573, 1.000391]]
+
+
+class TestHamiltonAR1SwitchTVTP(MarkovAutoregression):
+    @classmethod
+    def setup_class(cls):
+        # Results from E-views:
+        # Dependent variable followed by a list of switching regressors:
+        #     rgnp c ar(1)
+        # List of non-switching regressors: <blank>
+        # Do not check "Regime specific error variances"
+        # Switching type: Markov
+        # Number of Regimes: 2
+        # Probability regressors:
+        #     c recession
+        # Method SWITCHREG
+        # Sample 1951q1 1984q4
+        true = {
+            'params': np.r_[6.564923, 7.846371, -8.064123, -15.37636,
+                            1.027190, -0.719760,
+                            np.exp(-0.217003)**2, 0.161489, 0.022536],
+            'llf': -163.914049,
+            'llf_fit': -161.786477,
+            'llf_fit_em': -163.914049
+        }
+        exog_tvtp = np.c_[np.ones(len(rgnp)), rec]
+        super().setup_class(
+            true, rgnp, k_regimes=2, order=1, exog_tvtp=exog_tvtp)
+
+    @pytest.mark.skip  # TODO(ChadFulton): give reason for skip
+    def test_fit_em(self):
+        pass
+
+    def test_filtered_regimes(self):
+        assert_allclose(self.result.filtered_marginal_probabilities[:, 0],
+                        hamilton_ar1_switch_tvtp_filtered, atol=1e-5)
+
+    def test_smoothed_regimes(self):
+        assert_allclose(self.result.smoothed_marginal_probabilities[:, 0],
+                        hamilton_ar1_switch_tvtp_smoothed, atol=1e-5)
+
+    def test_expected_durations(self):
+        assert_allclose(self.result.expected_durations, expected_durations,
+                        rtol=1e-5, atol=1e-7)
+
+
+class TestFilardo(MarkovAutoregression):
+    @classmethod
+    def setup_class(cls):
+        path = os.path.join(current_path, 'results', 'mar_filardo.csv')
+        cls.mar_filardo = pd.read_csv(path)
+        true = {
+            'params': np.r_[4.35941747, -1.6493936, 1.7702123, 0.9945672,
+                            0.517298, -0.865888,
+                            np.exp(-0.362469)**2,
+                            0.189474, 0.079344, 0.110944, 0.122251],
+            'llf': -586.5718,
+            'llf_fit': -586.5718,
+            'llf_fit_em': -586.5718
+        }
+        endog = cls.mar_filardo['dlip'].iloc[1:].values
+        exog_tvtp = add_constant(
+            cls.mar_filardo['dmdlleading'].iloc[:-1].values)
+        super().setup_class(
+            true, endog, k_regimes=2, order=4, switching_ar=False,
+            exog_tvtp=exog_tvtp)
+
+    @pytest.mark.skip  # TODO(ChadFulton): give reason for skip
+    def test_fit(self, **kwargs):
+        pass
+
+    @pytest.mark.skip  # TODO(ChadFulton): give reason for skip
+    def test_fit_em(self):
+        pass
+
+    def test_filtered_regimes(self):
+        assert_allclose(self.result.filtered_marginal_probabilities[:, 0],
+                        self.mar_filardo['filtered_0'].iloc[5:], atol=1e-5)
+
+    def test_smoothed_regimes(self):
+        assert_allclose(self.result.smoothed_marginal_probabilities[:, 0],
+                        self.mar_filardo['smoothed_0'].iloc[5:], atol=1e-5)
+
+    def test_expected_durations(self):
+        assert_allclose(self.result.expected_durations,
+                        self.mar_filardo[['duration0', 'duration1']].iloc[5:],
+                        rtol=1e-5, atol=1e-7)
+
+
+class TestFilardoPandas(MarkovAutoregression):
+    @classmethod
+    def setup_class(cls):
+        path = os.path.join(current_path, 'results', 'mar_filardo.csv')
+        cls.mar_filardo = pd.read_csv(path)
+        cls.mar_filardo.index = pd.date_range('1948-02-01', '1991-04-01',
+                                              freq='MS')
+        true = {
+            'params': np.r_[4.35941747, -1.6493936, 1.7702123, 0.9945672,
+                            0.517298, -0.865888,
+                            np.exp(-0.362469)**2,
+                            0.189474, 0.079344, 0.110944, 0.122251],
+            'llf': -586.5718,
+            'llf_fit': -586.5718,
+            'llf_fit_em': -586.5718
+        }
+        endog = cls.mar_filardo['dlip'].iloc[1:]
+        exog_tvtp = add_constant(
+            cls.mar_filardo['dmdlleading'].iloc[:-1])
+        super().setup_class(
+            true, endog, k_regimes=2, order=4, switching_ar=False,
+            exog_tvtp=exog_tvtp)
+
+    @pytest.mark.skip  # TODO(ChadFulton): give reason for skip
+    def test_fit(self, **kwargs):
+        pass
+
+    @pytest.mark.skip  # TODO(ChadFulton): give reason for skip
+    def test_fit_em(self):
+        pass
+
+    def test_filtered_regimes(self):
+        assert_allclose(self.result.filtered_marginal_probabilities[0],
+                        self.mar_filardo['filtered_0'].iloc[5:], atol=1e-5)
+
+    def test_smoothed_regimes(self):
+        assert_allclose(self.result.smoothed_marginal_probabilities[0],
+                        self.mar_filardo['smoothed_0'].iloc[5:], atol=1e-5)
+
+    def test_expected_durations(self):
+        assert_allclose(self.result.expected_durations,
+                        self.mar_filardo[['duration0', 'duration1']].iloc[5:],
+                        rtol=1e-5, atol=1e-7)

venv/lib/python3.11/site-packages/statsmodels/tsa/regime_switching/tests/test_markov_switching.py

@@ -0,0 +1,317 @@
+"""
+General tests for Markov switching models
+
+Author: Chad Fulton
+License: BSD-3
+"""
+
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose, assert_raises
+import pandas as pd
+
+from statsmodels.tools.numdiff import approx_fprime_cs
+from statsmodels.tsa.regime_switching import markov_switching
+
+
+def test_params():
+    def check_transtion_2(params):
+        assert_equal(params['regime_transition'], np.s_[0:2])
+        assert_equal(params[0, 'regime_transition'], [0])
+        assert_equal(params[1, 'regime_transition'], [1])
+        assert_equal(params['regime_transition', 0], [0])
+        assert_equal(params['regime_transition', 1], [1])
+
+    def check_transition_3(params):
+        assert_equal(params['regime_transition'], np.s_[0:6])
+        assert_equal(params[0, 'regime_transition'], [0, 3])
+        assert_equal(params[1, 'regime_transition'], [1, 4])
+        assert_equal(params[2, 'regime_transition'], [2, 5])
+        assert_equal(params['regime_transition', 0], [0, 3])
+        assert_equal(params['regime_transition', 1], [1, 4])
+        assert_equal(params['regime_transition', 2], [2, 5])
+
+    params = markov_switching.MarkovSwitchingParams(k_regimes=2)
+    params['regime_transition'] = [1]
+    assert_equal(params.k_params, 1 * 2)
+    assert_equal(params[0], [0])
+    assert_equal(params[1], [1])
+    check_transtion_2(params)
+
+    params['exog'] = [0, 1]
+    assert_equal(params.k_params, 1 * 2 + 1 + 1 * 2)
+    assert_equal(params[0], [0, 2, 3])
+    assert_equal(params[1], [1, 2, 4])
+    check_transtion_2(params)
+    assert_equal(params['exog'], np.s_[2:5])
+    assert_equal(params[0, 'exog'], [2, 3])
+    assert_equal(params[1, 'exog'], [2, 4])
+    assert_equal(params['exog', 0], [2, 3])
+    assert_equal(params['exog', 1], [2, 4])
+
+    params = markov_switching.MarkovSwitchingParams(k_regimes=3)
+    params['regime_transition'] = [1, 1]
+    assert_equal(params.k_params, 2 * 3)
+    assert_equal(params[0], [0, 3])
+    assert_equal(params[1], [1, 4])
+    assert_equal(params[2], [2, 5])
+    check_transition_3(params)
+
+    # Test for invalid parameter setting
+    assert_raises(IndexError, params.__setitem__, None, [1, 1])
+
+    # Test for invalid parameter selection
+    assert_raises(IndexError, params.__getitem__, None)
+    assert_raises(IndexError, params.__getitem__, (0, 0))
+    assert_raises(IndexError, params.__getitem__, ('exog', 'exog'))
+    assert_raises(IndexError, params.__getitem__, ('exog', 0, 1))
+
+
+def test_init_endog():
+    index = pd.date_range(start='1950-01-01', periods=10, freq='D')
+    endog = [
+        np.ones(10), pd.Series(np.ones(10), index=index), np.ones((10, 1)),
+        pd.DataFrame(np.ones((10, 1)), index=index)
+    ]
+    for _endog in endog:
+        mod = markov_switching.MarkovSwitching(_endog, k_regimes=2)
+        assert_equal(mod.nobs, 10)
+        assert_equal(mod.endog, _endog.squeeze())
+        assert_equal(mod.k_regimes, 2)
+        assert_equal(mod.tvtp, False)
+        assert_equal(mod.k_tvtp, 0)
+        assert_equal(mod.k_params, 2)
+
+    # Invalid: k_regimes < 2
+    endog = np.ones(10)
+    assert_raises(ValueError, markov_switching.MarkovSwitching, endog,
+                  k_regimes=1)
+
+    # Invalid: multiple endog columns
+    endog = np.ones((10, 2))
+    assert_raises(ValueError, markov_switching.MarkovSwitching, endog,
+                  k_regimes=2)
+
+
+def test_init_exog_tvtp():
+    endog = np.ones(10)
+    exog_tvtp = np.c_[np.ones((10, 1)), (np.arange(10) + 1)[:, np.newaxis]]
+    mod = markov_switching.MarkovSwitching(endog, k_regimes=2,
+                                           exog_tvtp=exog_tvtp)
+    assert_equal(mod.tvtp, True)
+    assert_equal(mod.k_tvtp, 2)
+
+    # Invalid exog_tvtp (too many obs)
+    exog_tvtp = np.c_[np.ones((11, 1)), (np.arange(11) + 1)[:, np.newaxis]]
+    assert_raises(ValueError, markov_switching.MarkovSwitching, endog,
+                  k_regimes=2, exog_tvtp=exog_tvtp)
+
+
+def test_transition_matrix():
+    # k_regimes = 2
+    endog = np.ones(10)
+    mod = markov_switching.MarkovSwitching(endog, k_regimes=2)
+    params = np.r_[0., 0., 1.]
+    transition_matrix = np.zeros((2, 2, 1))
+    transition_matrix[1, :] = 1.
+    assert_allclose(mod.regime_transition_matrix(params), transition_matrix)
+
+    # k_regimes = 3
+    endog = np.ones(10)
+    mod = markov_switching.MarkovSwitching(endog, k_regimes=3)
+    params = np.r_[[0]*3, [0.2]*3, 1.]
+    transition_matrix = np.zeros((3, 3, 1))
+    transition_matrix[1, :, 0] = 0.2
+    transition_matrix[2, :, 0] = 0.8
+    assert_allclose(mod.regime_transition_matrix(params), transition_matrix)
+
+    # k_regimes = 2, tvtp
+    endog = np.ones(10)
+    exog_tvtp = np.c_[np.ones((10, 1)), (np.arange(10) + 1)[:, np.newaxis]]
+    mod = markov_switching.MarkovSwitching(endog, k_regimes=2,
+                                           exog_tvtp=exog_tvtp)
+
+    # If all TVTP regression coefficients are zero, then the logit transform
+    # results in exp(0) / (1 + exp(0)) = 0.5 for all parameters; since it's
+    # k_regimes=2 the remainder calculation is also 0.5.
+    params = np.r_[0, 0, 0, 0]
+    assert_allclose(mod.regime_transition_matrix(params), 0.5)
+
+    # Manually compute the TVTP coefficients
+    params = np.r_[1, 2, 1, 2]
+    transition_matrix = np.zeros((2, 2, 10))
+
+    coeffs0 = np.sum(exog_tvtp, axis=1)
+    p11 = np.exp(coeffs0) / (1 + np.exp(coeffs0))
+    transition_matrix[0, 0, :] = p11
+    transition_matrix[1, 0, :] = 1 - p11
+
+    coeffs1 = np.sum(2 * exog_tvtp, axis=1)
+    p21 = np.exp(coeffs1) / (1 + np.exp(coeffs1))
+    transition_matrix[0, 1, :] = p21
+    transition_matrix[1, 1, :] = 1 - p21
+    assert_allclose(mod.regime_transition_matrix(params), transition_matrix,
+                    atol=1e-10)
+
+    # k_regimes = 3, tvtp
+    endog = np.ones(10)
+    exog_tvtp = np.c_[np.ones((10, 1)), (np.arange(10) + 1)[:, np.newaxis]]
+    mod = markov_switching.MarkovSwitching(
+        endog, k_regimes=3, exog_tvtp=exog_tvtp)
+
+    # If all TVTP regression coefficients are zero, then the logit transform
+    # results in exp(0) / (1 + exp(0) + exp(0)) = 1/3 for all parameters;
+    # since it's k_regimes=3 the remainder calculation is also 1/3.
+    params = np.r_[[0]*12]
+    assert_allclose(mod.regime_transition_matrix(params), 1 / 3)
+
+    # Manually compute the TVTP coefficients for the first column
+    params = np.r_[[0]*6, [2]*6]
+    transition_matrix = np.zeros((3, 3, 10))
+
+    p11 = np.zeros(10)
+    p12 = 2 * np.sum(exog_tvtp, axis=1)
+    tmp = np.exp(np.c_[p11, p12]).T
+    transition_matrix[:2, 0, :] = tmp / (1 + np.sum(tmp, axis=0))
+    transition_matrix[2, 0, :] = (
+        1 - np.sum(transition_matrix[:2, 0, :], axis=0))
+    assert_allclose(mod.regime_transition_matrix(params)[:, 0, :],
+                    transition_matrix[:, 0, :], atol=1e-10)
+
+
+def test_initial_probabilities():
+    endog = np.ones(10)
+    mod = markov_switching.MarkovSwitching(endog, k_regimes=2)
+    params = np.r_[0.5, 0.5, 1.]
+
+    # Valid known initial probabilities
+    mod.initialize_known([0.2, 0.8])
+    assert_allclose(mod.initial_probabilities(params), [0.2, 0.8])
+
+    # Invalid known initial probabilities (too many elements)
+    assert_raises(ValueError, mod.initialize_known, [0.2, 0.2, 0.6])
+
+    # Invalid known initial probabilities (does not sum to 1)
+    assert_raises(ValueError, mod.initialize_known, [0.2, 0.2])
+
+    # Valid steady-state probabilities
+    mod.initialize_steady_state()
+    assert_allclose(mod.initial_probabilities(params), [0.5, 0.5])
+
+    # Invalid steady-state probabilities (when mod has tvtp)
+    endog = np.ones(10)
+    mod = markov_switching.MarkovSwitching(endog, k_regimes=2, exog_tvtp=endog)
+    assert_raises(ValueError, mod.initialize_steady_state)
+
+
+def test_logistic():
+    logistic = markov_switching._logistic
+
+    # For a number, logistic(x) = np.exp(x) / (1 + np.exp(x))
+    cases = [0, 10., -4]
+    for x in cases:
+        # Have to use allclose b/c logistic() actually uses logsumexp, so
+        # they're not equal
+        assert_allclose(logistic(x), np.exp(x) / (1 + np.exp(x)))
+
+    # For a vector, logistic(x) returns
+    # np.exp(x[i]) / (1 + np.sum(np.exp(x[:]))) for each i
+    # but squeezed
+    cases = [[1.], [0, 1.], [-2, 3., 1.2, -30.]]
+    for x in cases:
+        actual = logistic(x)
+        desired = [np.exp(i) / (1 + np.sum(np.exp(x))) for i in x]
+        assert_allclose(actual, desired)
+
+    # For a 2-dim, logistic(x) returns
+    # np.exp(x[i, t]) / (1 + np.sum(np.exp(x[:, t]))) for each i, each t
+    # but squeezed
+    case = [[1.]]
+    actual = logistic(case)
+    assert_equal(actual.shape, (1, 1))
+    assert_allclose(actual, np.exp(1) / (1 + np.exp(1)))
+
+    # Here, np.array(case) is 2x1, so it is interpreted as i=0, 1 and t=0
+    case = [[0], [1.]]
+    actual = logistic(case)
+    desired = [np.exp(i) / (1 + np.sum(np.exp(case))) for i in case]
+    assert_allclose(actual, desired)
+
+    # Here, np.array(case) is 1x2, so it is interpreted as i=0 and t=0, 1
+    case = [[0, 1.]]
+    actual = logistic(case)
+    desired = np.exp(case) / (1 + np.exp(case))
+    assert_allclose(actual, desired)
+
+    # For a 3-dim, logistic(x) returns
+    # np.exp(x[i, j, t]) / (1 + np.sum(np.exp(x[:, j, t])))
+    # for each i, each j, each t
+    case = np.arange(2*3*4).reshape(2, 3, 4)
+    actual = logistic(case)
+    for j in range(3):
+        assert_allclose(actual[:, j, :], logistic(case[:, j, :]))
+
+
+def test_partials_logistic():
+    # Here we compare to analytic derivatives and to finite-difference
+    # approximations
+    logistic = markov_switching._logistic
+    partials_logistic = markov_switching._partials_logistic
+
+    # For a number, logistic(x) = np.exp(x) / (1 + np.exp(x))
+    # Then d/dx = logistix(x) - logistic(x)**2
+    cases = [0, 10., -4]
+    for x in cases:
+        assert_allclose(partials_logistic(x), logistic(x) - logistic(x)**2)
+        assert_allclose(partials_logistic(x), approx_fprime_cs([x], logistic))
+
+    # For a vector, logistic(x) returns
+    # np.exp(x[i]) / (1 + np.sum(np.exp(x[:]))) for each i
+    # Then d logistic(x[i]) / dx[i] = (logistix(x) - logistic(x)**2)[i]
+    # And d logistic(x[i]) / dx[j] = -(logistic(x[i]) * logistic[x[j]])
+    cases = [[1.], [0, 1.], [-2, 3., 1.2, -30.]]
+    for x in cases:
+        evaluated = np.atleast_1d(logistic(x))
+        partials = np.diag(evaluated - evaluated**2)
+        for i in range(len(x)):
+            for j in range(i):
+                partials[i, j] = partials[j, i] = -evaluated[i] * evaluated[j]
+        assert_allclose(partials_logistic(x), partials)
+        assert_allclose(partials_logistic(x), approx_fprime_cs(x, logistic))
+
+    # For a 2-dim, logistic(x) returns
+    # np.exp(x[i, t]) / (1 + np.sum(np.exp(x[:, t]))) for each i, each t
+    # but squeezed
+    case = [[1.]]
+    evaluated = logistic(case)
+    partial = [evaluated - evaluated**2]
+    assert_allclose(partials_logistic(case), partial)
+    assert_allclose(partials_logistic(case), approx_fprime_cs(case, logistic))
+
+    # # Here, np.array(case) is 2x1, so it is interpreted as i=0, 1 and t=0
+    case = [[0], [1.]]
+    evaluated = logistic(case)[:, 0]
+    partials = np.diag(evaluated - evaluated**2)
+    partials[0, 1] = partials[1, 0] = -np.multiply(*evaluated)
+    assert_allclose(partials_logistic(case)[:, :, 0], partials)
+    assert_allclose(partials_logistic(case),
+                    approx_fprime_cs(np.squeeze(case), logistic)[..., None])
+
+    # Here, np.array(case) is 1x2, so it is interpreted as i=0 and t=0, 1
+    case = [[0, 1.]]
+    evaluated = logistic(case)
+    partials = (evaluated - evaluated**2)[None, ...]
+    assert_allclose(partials_logistic(case), partials)
+    assert_allclose(partials_logistic(case),
+                    approx_fprime_cs(case, logistic).T)
+
+    # For a 3-dim, logistic(x) returns
+    # np.exp(x[i, j, t]) / (1 + np.sum(np.exp(x[:, j, t])))
+    # for each i, each j, each t
+    case = np.arange(2*3*4).reshape(2, 3, 4)
+    evaluated = logistic(case)
+    partials = partials_logistic(case)
+    for t in range(4):
+        for j in range(3):
+            desired = np.diag(evaluated[:, j, t] - evaluated[:, j, t]**2)
+            desired[0, 1] = desired[1, 0] = -np.multiply(*evaluated[:, j, t])
+            assert_allclose(partials[..., j, t], desired)