# 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