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
  • endog (array_like) – The endogenous variable.

  • k_regimes (integer) – The number of regimes.

  • order (integer) – The order of the autoregressive lag polynomial.

  • trend ({'nc', '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=’nc’. 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 (boolean 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 (boolean 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 (boolean 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 (boolean, 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 accomodated 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.

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 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

Attributes

endog_names

Names of endogenous variables

exog_names

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.