statsmodels.tsa.regime_switching.markov_autoregression.MarkovAutoregression¶

class statsmodels.tsa.regime_switching.markov_autoregression.MarkovAutoregression(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')[source]

Markov switching regression model

Parameters:
endogarray_like

The endogenous variable.

k_regimesint

The number of regimes.

orderint

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.

exogarray_like, optional

Array of exogenous regressors, shaped nobs x k.

exog_tvtparray_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_arbool 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_trendbool 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_exogbool 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_variancebool, 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:

$\begin{split}y_t = a_{S_t} + x_t' \beta_{S_t} + \phi_{1, S_t} (y_{t-1} - a_{S_{t-1}} - x_{t-1}' \beta_{S_{t-1}}) + \dots + \phi_{p, S_t} (y_{t-p} - a_{S_{t-p}} - x_{t-p}' \beta_{S_{t-p}}) + \varepsilon_t \\ \varepsilon_t \sim N(0, \sigma_{S_t}^2)\end{split}$

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 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.

Attributes:
endog_names

Names of endogenous variables.

exog_names

The names of the exogenous variables.

k_params

(int) Number of parameters in the model

param_names

(list of str) List of human readable parameter names (for parameters

start_params

(array) Starting parameters for maximum likelihood estimation.

Methods

 filter(params[, transformed, cov_type, ...]) Apply the Hamilton filter fit([start_params, transformed, cov_type, ...]) Fits the model by maximum likelihood via Hamilton filter. from_formula(formula, data[, subset, drop_cols]) Create a Model from a formula and dataframe. hessian(params[, transformed]) Hessian matrix of the likelihood function, evaluated at the given parameters information(params) Fisher information matrix of model. initial_probabilities(params[, ...]) Retrieve initial probabilities Initialize (possibly re-initialize) a Model instance. initialize_known(probabilities[, tol]) Set initialization of regime probabilities to use known values Set initialization of regime probabilities to be steady-state values loglike(params[, transformed]) Loglikelihood evaluation loglikeobs(params[, transformed]) Loglikelihood evaluation for each period predict(params[, start, end, probabilities, ...]) In-sample prediction and out-of-sample forecasting predict_conditional(params) In-sample prediction, conditional on the current and previous regime regime_transition_matrix(params[, exog_tvtp]) Construct the left-stochastic transition matrix score(params[, transformed]) Compute the score function at params. score_obs(params[, transformed]) Compute the score per observation, evaluated at params smooth(params[, transformed, cov_type, ...]) Apply the Kim smoother and Hamilton filter transform_params(unconstrained) Transform unconstrained parameters used by the optimizer to constrained parameters used in likelihood evaluation untransform_params(constrained) Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer

Properties

 endog_names Names of endogenous variables. exog_names The names of the exogenous variables. k_params (int) Number of parameters in the model param_names (list of str) List of human readable parameter names (for parameters actually included in the model). start_params (array) Starting parameters for maximum likelihood estimation.