statsmodels.tsa.regime_switching.markov_regression.MarkovRegression

class statsmodels.tsa.regime_switching.markov_regression.MarkovRegression(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')[source]

First-order k-regime Markov switching regression model

Parameters
endogarray_like

The endogenous variable.

k_regimesint

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.

exogarray_like, optional

Array of exogenous regressors, shaped nobs x k.

orderint, 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_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_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:

\[\begin{split}y_t = a_{S_t} + x_t' \beta_{S_t} + \varepsilon_t \\ \varepsilon_t \sim N(0, \sigma_{S_t}^2)\end{split}\]

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.

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()

Initialize (possibly re-initialize) a Model instance.

initialize_known(probabilities[, tol])

Set initialization of regime probabilities to use known values

initialize_steady_state()

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 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.