statsmodels.tsa.statespace.mlemodel.MLEModel

class statsmodels.tsa.statespace.mlemodel.MLEModel(endog, k_states, exog=None, dates=None, freq=None, **kwargs)[source]

State space model for maximum likelihood estimation

Parameters
endogarray_like

The observed time-series process \(y\)

k_statesint

The dimension of the unobserved state process.

exogarray_like, optional

Array of exogenous regressors, shaped nobs x k. Default is no exogenous regressors.

datesarray_like of datetime, optional

An array-like object of datetime objects. If a Pandas object is given for endog, it is assumed to have a DateIndex.

freqstr, optional

The frequency of the time-series. A Pandas offset or ‘B’, ‘D’, ‘W’, ‘M’, ‘A’, or ‘Q’. This is optional if dates are given.

**kwargs

Keyword arguments may be used to provide default values for state space matrices or for Kalman filtering options. See Representation, and KalmanFilter for more details.

Notes

This class wraps the state space model with Kalman filtering to add in functionality for maximum likelihood estimation. In particular, it adds the concept of updating the state space representation based on a defined set of parameters, through the update method or updater attribute (see below for more details on which to use when), and it adds a fit method which uses a numerical optimizer to select the parameters that maximize the likelihood of the model.

The start_params update method must be overridden in the child class (and the transform and untransform methods, if needed).

Attributes
ssmstatsmodels.tsa.statespace.kalman_filter.KalmanFilter

Underlying state space representation.

Methods

clone(endog[, exog])

Clone state space model with new data and optionally new specification

filter(params[, transformed, ...])

Kalman filtering

fit([start_params, transformed, ...])

Fits the model by maximum likelihood via Kalman filter.

fit_constrained(constraints[, start_params])

Fit the model with some parameters subject to equality constraints.

fix_params(params)

Fix parameters to specific values (context manager)

from_formula(formula, data[, subset])

Not implemented for state space models

handle_params(params[, transformed, ...])

Ensure model parameters satisfy shape and other requirements

hessian(params, *args, **kwargs)

Hessian matrix of the likelihood function, evaluated at the given parameters

impulse_responses(params[, steps, impulse, ...])

Impulse response function

information(params)

Fisher information matrix of model.

initialize()

Initialize (possibly re-initialize) a Model instance.

initialize_approximate_diffuse([variance])

Initialize approximate diffuse

initialize_known(initial_state, ...)

Initialize known

initialize_statespace(**kwargs)

Initialize the state space representation

initialize_stationary()

Initialize stationary

loglike(params, *args, **kwargs)

Loglikelihood evaluation

loglikeobs(params[, transformed, ...])

Loglikelihood evaluation

observed_information_matrix(params[, ...])

Observed information matrix

opg_information_matrix(params[, ...])

Outer product of gradients information matrix

predict(params[, exog])

After a model has been fit predict returns the fitted values.

prepare_data()

Prepare data for use in the state space representation

score(params, *args, **kwargs)

Compute the score function at params.

score_obs(params[, method, transformed, ...])

Compute the score per observation, evaluated at params

set_conserve_memory([conserve_memory])

Set the memory conservation method

set_filter_method([filter_method])

Set the filtering method

set_inversion_method([inversion_method])

Set the inversion method

set_smoother_output([smoother_output])

Set the smoother output

set_stability_method([stability_method])

Set the numerical stability method

simulate(params, nsimulations[, ...])

Simulate a new time series following the state space model

simulation_smoother([simulation_output])

Retrieve a simulation smoother for the state space model.

smooth(params[, transformed, ...])

Kalman smoothing

transform_jacobian(unconstrained[, ...])

Jacobian matrix for the parameter transformation function

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

update(params[, transformed, ...])

Update the parameters of the model

Properties

endog_names

Names of endogenous variables.

exog_names

The names of the exogenous variables.

initial_variance

initialization

loglikelihood_burn

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.

state_names

(list of str) List of human readable names for unobserved states.

tolerance