statsmodels.tsa.statespace.kalman_smoother.SmootherResults

class statsmodels.tsa.statespace.kalman_smoother.SmootherResults(model)[source]

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

Parameters:model (Representation) – A Statespace representation
nobs

Number of observations.

Type:int
k_endog

The dimension of the observation series.

Type:int
k_states

The dimension of the unobserved state process.

Type:int
k_posdef

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

Type:int
dtype

Datatype of representation matrices

Type:dtype
prefix

BLAS prefix of representation matrices

Type:str
shapes

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

Type:dictionary of name:tuple
endog

The observation vector.

Type:array
design

The design matrix, \(Z\).

Type:array
obs_intercept

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

Type:array
obs_cov

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

Type:array
transition

The transition matrix, \(T\).

Type:array
state_intercept

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

Type:array
selection

The selection matrix, \(R\).

Type:array
state_cov

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

Type:array
missing

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.

Type:array of bool
nmissing

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.

Type:array of int
time_invariant

Whether or not the representation matrices are time-invariant

Type:bool
initialization

Kalman filter initialization method.

Type:str
initial_state

The state vector used to initialize the Kalamn filter.

Type:array_like
initial_state_cov

The state covariance matrix used to initialize the Kalamn filter.

Type:array_like
filter_method

Bitmask representing the Kalman filtering method

Type:int
inversion_method

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

Type:int
stability_method

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

Type:int
conserve_memory

Bitmask representing the selected memory conservation method.

Type:int
tolerance

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

Type:float
loglikelihood_burn

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

Type:int
converged

Whether or not the Kalman filter converged.

Type:bool
period_converged

The time period in which the Kalman filter converged.

Type:int
filtered_state

The filtered state vector at each time period.

Type:array
filtered_state_cov

The filtered state covariance matrix at each time period.

Type:array
predicted_state

The predicted state vector at each time period.

Type:array
predicted_state_cov

The predicted state covariance matrix at each time period.

Type:array
kalman_gain

The Kalman gain at each time period.

Type:array
forecasts

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

Type:array
forecasts_error

The forecast errors at each time period.

Type:array
forecasts_error_cov

The forecast error covariance matrices at each time period.

Type:array
loglikelihood

The loglikelihood values at each time period.

Type:array
collapsed_forecasts

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

Type:array
collapsed_forecasts_error

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

Type:array
collapsed_forecasts_error_cov

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

Type:array
standardized_forecast_error

The standardized forecast errors

Type:array
smoother_output

Bitmask representing the generated Kalman smoothing output

Type:int
scaled_smoothed_estimator

The scaled smoothed estimator at each time period.

Type:array
scaled_smoothed_estimator_cov

The scaled smoothed estimator covariance matrices at each time period.

Type:array
smoothing_error

The smoothing error covariance matrices at each time period.

Type:array
smoothed_state

The smoothed state at each time period.

Type:array
smoothed_state_cov

The smoothed state covariance matrices at each time period.

Type:array
smoothed_state_autocov

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

Type:array
smoothed_measurement_disturbance

The smoothed measurement at each time period.

Type:array
smoothed_state_disturbance

The smoothed state at each time period.

Type:array
smoothed_measurement_disturbance_cov

The smoothed measurement disturbance covariance matrices at each time period.

Type:array
smoothed_state_disturbance_cov

The smoothed state disturbance covariance matrices at each time period.

Type:array

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