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:model (Representation) – A Statespace representation

nobs

int – Number of observations.

k_endog

int – The dimension of the observation series.

k_states

int – The dimension of the unobserved state process.

k_posdef

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

dtype

dtype – Datatype of representation matrices

prefix

str – BLAS prefix of representation matrices

shapes

dictionary of name:tuple – A dictionary recording the shapes of each of the representation matrices as tuples.

endog

array – The observation vector.

design

array – The design matrix, \(Z\).

obs_intercept

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

obs_cov

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

transition

array – The transition matrix, \(T\).

state_intercept

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

selection

array – The selection matrix, \(R\).

state_cov

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

missing

array 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.

nmissing

array 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_invariant

bool – Whether or not the representation matrices are time-invariant

initialization

str – Kalman filter initialization method.

initial_state

array_like – The state vector used to initialize the Kalamn filter.

initial_state_cov

array_like – The state covariance matrix used to initialize the Kalamn filter.

filter_method

int – Bitmask representing the Kalman filtering method

inversion_method

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

stability_method

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

conserve_memory

int – Bitmask representing the selected memory conservation method.

tolerance

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

loglikelihood_burn

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

converged

bool – Whether or not the Kalman filter converged.

period_converged

int – The time period in which the Kalman filter converged.

filtered_state

array – The filtered state vector at each time period.

filtered_state_cov

array – The filtered state covariance matrix at each time period.

predicted_state

array – The predicted state vector at each time period.

predicted_state_cov

array – The predicted state covariance matrix at each time period.

kalman_gain

array – The Kalman gain at each time period.

forecasts

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

forecasts_error

array – The forecast errors at each time period.

forecasts_error_cov

array – The forecast error covariance matrices at each time period.

loglikelihood

array – The loglikelihood values at each time period.

collapsed_forecasts

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

collapsed_forecasts_error

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

collapsed_forecasts_error_cov

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

standardized_forecast_error

array – The standardized forecast errors

smoother_output

int – Bitmask representing the generated Kalman smoothing output

scaled_smoothed_estimator

array – The scaled smoothed estimator at each time period.

scaled_smoothed_estimator_cov

array – The scaled smoothed estimator covariance matrices at each time period.

smoothing_error

array – The smoothing error covariance matrices at each time period.

smoothed_state

array – The smoothed state at each time period.

smoothed_state_cov

array – The smoothed state covariance matrices at each time period.

smoothed_state_autocov

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

smoothed_measurement_disturbance

array – The smoothed measurement at each time period.

smoothed_state_disturbance

array – The smoothed state at each time period.

smoothed_measurement_disturbance_cov

array – The smoothed measurement disturbance covariance matrices at each time period.

smoothed_state_disturbance_cov

array – 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

Attributes

kalman_gain	Kalman gain matrices
smoothed_forecasts
smoothed_forecasts_error
smoothed_forecasts_error_cov
standardized_forecasts_error	Standardized forecast errors