statsmodels.tsa.statespace.kalman_smoother.SmootherResults

class statsmodels.tsa.statespace.kalman_smoother.SmootherResults(model)

Results from applying the Kalman smoother and/or filter to a state space model.

Parameters

modelRepresentation

A Statespace representation

Attributes

nobsint

Number of observations.

k_endogint

The dimension of the observation series.

k_statesint

The dimension of the unobserved state process.

k_posdefint

The dimension of a guaranteed positive definite covariance matrix describing the shocks in the measurement equation.

dtypedtype

Datatype of representation matrices

prefixstr

BLAS prefix of representation matrices

shapesdictionary of name:tuple

A dictionary recording the shapes of each of the representation matrices as tuples.

endogarray

The observation vector.

designarray

The design matrix, \(Z\).

obs_interceptarray

The intercept for the observation equation, \(d\).

obs_covarray

The covariance matrix for the observation equation \(H\).

transitionarray

The transition matrix, \(T\).

state_interceptarray

The intercept for the transition equation, \(c\).

selectionarray

The selection matrix, \(R\).

state_covarray

The covariance matrix for the state equation \(Q\).

missingarray of bool

An array of the same size as endog, filled with boolean values that are True if the corresponding entry in endog is NaN and False otherwise.

nmissingarray of int

An array of size nobs, where the ith entry is the number (between 0 and k_endog) of NaNs in the ith row of the endog array.

time_invariantbool

Whether or not the representation matrices are time-invariant

initializationstr

Kalman filter initialization method.

initial_statearray_like

The state vector used to initialize the Kalamn filter.

initial_state_covarray_like

The state covariance matrix used to initialize the Kalamn filter.

filter_methodint

Bitmask representing the Kalman filtering method

inversion_methodint

Bitmask representing the method used to invert the forecast error covariance matrix.

stability_methodint

Bitmask representing the methods used to promote numerical stability in the Kalman filter recursions.

conserve_memoryint

Bitmask representing the selected memory conservation method.

tolerancefloat

The tolerance at which the Kalman filter determines convergence to steady-state.

loglikelihood_burnint

The number of initial periods during which the loglikelihood is not recorded.

convergedbool

Whether or not the Kalman filter converged.

period_convergedint

The time period in which the Kalman filter converged.

filtered_statearray

The filtered state vector at each time period.

filtered_state_covarray

The filtered state covariance matrix at each time period.

predicted_statearray

The predicted state vector at each time period.

predicted_state_covarray

The predicted state covariance matrix at each time period.

kalman_gainarray

Kalman gain matrices

forecastsarray

The one-step-ahead forecasts of observations at each time period.

forecasts_errorarray

The forecast errors at each time period.

forecasts_error_covarray

The forecast error covariance matrices at each time period.

loglikelihoodarray

The loglikelihood values at each time period.

collapsed_forecastsarray

If filtering using collapsed observations, stores the one-step-ahead forecasts of collapsed observations at each time period.

collapsed_forecasts_errorarray

If filtering using collapsed observations, stores the one-step-ahead forecast errors of collapsed observations at each time period.

collapsed_forecasts_error_covarray

If filtering using collapsed observations, stores the one-step-ahead forecast error covariance matrices of collapsed observations at each time period.

standardized_forecast_errorarray

The standardized forecast errors

smoother_outputint

Bitmask representing the generated Kalman smoothing output

scaled_smoothed_estimatorarray

The scaled smoothed estimator at each time period.

scaled_smoothed_estimator_covarray

The scaled smoothed estimator covariance matrices at each time period.

smoothing_errorarray

The smoothing error covariance matrices at each time period.

smoothed_statearray

The smoothed state at each time period.

smoothed_state_covarray

The smoothed state covariance matrices at each time period.

smoothed_state_autocovarray

The smoothed state lago-one autocovariance matrices at each time period: \(Cov(\alpha_{t+1}, \alpha_t)\).

smoothed_measurement_disturbancearray

The smoothed measurement at each time period.

smoothed_state_disturbancearray

The smoothed state at each time period.

smoothed_measurement_disturbance_covarray

The smoothed measurement disturbance covariance matrices at each time period.

smoothed_state_disturbance_covarray

The smoothed state disturbance covariance matrices at each time period.

Methods

predict([start, end, dynamic])	In-sample and out-of-sample prediction for state space models generally
update_filter(kalman_filter)	Update the filter results
update_representation(model[, only_options])	Update the results to match a given model
update_smoother(smoother)	Update the smoother results

Properties

kalman_gain	Kalman gain matrices
smoothed_forecasts
smoothed_forecasts_error
smoothed_forecasts_error_cov
standardized_forecasts_error	Standardized forecast errors