statsmodels.tsa.statespace.kalman_smoother.KalmanSmoother

class statsmodels.tsa.statespace.kalman_smoother.KalmanSmoother(k_endog, k_states, k_posdef=None, results_class=None, kalman_smoother_classes=None, **kwargs)

State space representation of a time series process, with Kalman filter and smoother.

Parameters:

k_endog{array_like, int}

The observed time-series process \(y\) if array like or the number of variables in the process if an integer.

k_statesint

The dimension of the unobserved state process.

k_posdefint, optional

The dimension of a guaranteed positive definite covariance matrix describing the shocks in the measurement equation. Must be less than or equal to k_states. Default is k_states.

results_classclass, optional

Default results class to use to save filtering output. Default is SmootherResults. If specified, class must extend from SmootherResults.

**kwargs

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

Attributes:

design

dtype

(dtype) Datatype of currently active representation matrices

endog

memory_no_filtered

(bool) Flag to prevent storing filtered state and covariance matrices.

memory_no_forecast

(bool) Flag to prevent storing all forecast-related output.

memory_no_predicted

(bool) Flag to prevent storing predicted state and covariance matrices.

obs

(array) Observation vector: \(y~(k\_endog \times nobs)\)

obs_cov

obs_intercept

prefix

(str) BLAS prefix of currently active representation matrices

selection

state_cov

state_intercept

time_invariant

(bool) Whether or not currently active representation matrices are

transition

Methods

bind(endog)	Bind data to the statespace representation
clone(endog, **kwargs)	Clone a state space representation while overriding some elements
diff_endog(new_endog[, tolerance])
extend(endog[, start, end])	Extend the current state space model, or a specific (time) subset
filter([filter_method, inversion_method, ...])	Apply the Kalman filter to the statespace model.
fixed_scale(scale)	Context manager for fixing the scale when FILTER_CONCENTRATED is set
impulse_responses([steps, impulse, ...])	Impulse response function
initialize(initialization[, ...])	Create an Initialization object if necessary
initialize_approximate_diffuse([variance])	Initialize the statespace model with approximate diffuse values.
initialize_diffuse()	Initialize the statespace model as stationary.
initialize_known(constant, stationary_cov)	Initialize the statespace model with known distribution for initial state.
initialize_stationary()	Initialize the statespace model as stationary.
loglike(**kwargs)	Calculate the loglikelihood associated with the statespace model.
loglikeobs(**kwargs)	Calculate the loglikelihood for each observation associated with the statespace model.
set_conserve_memory([conserve_memory])	Set the memory conservation method
set_filter_method([filter_method])	Set the filtering method
set_filter_timing([alternate_timing])	Set the filter timing convention
set_inversion_method([inversion_method])	Set the inversion method
set_smooth_method([smooth_method])	Set the smoothing method
set_smoother_output([smoother_output])	Set the smoother output
set_stability_method([stability_method])	Set the numerical stability method
simulate(nsimulations[, measurement_shocks, ...])	Simulate a new time series following the state space model
smooth([smoother_output, smooth_method, ...])	Apply the Kalman smoother to the statespace model.

Properties

conserve_memory	(int) Memory conservation bitmask.
design	(array) Design matrix: \(Z~(k\_endog \times k\_states \times nobs)\)
dtype	(dtype) Datatype of currently active representation matrices
endog	(array) The observation vector, alias for obs.
filter_augmented	(bool) Flag for augmented Kalman filtering.
filter_chandrasekhar	(bool) Flag for filtering with Chandrasekhar recursions.
filter_collapsed	(bool) Flag for Kalman filtering with collapsed observation vector.
filter_concentrated	(bool) Flag for Kalman filtering with concentrated log-likelihood.
filter_conventional	(bool) Flag for conventional Kalman filtering.
filter_exact_initial	(bool) Flag for exact initial Kalman filtering.
filter_extended	(bool) Flag for extended Kalman filtering.
filter_method	(int) Filtering method bitmask.
filter_methods
filter_square_root	(bool) Flag for square-root Kalman filtering.
filter_timing	(int) Filter timing.
filter_univariate	(bool) Flag for univariate filtering of multivariate observation vector.
filter_unscented	(bool) Flag for unscented Kalman filtering.
inversion_method	(int) Inversion method bitmask.
inversion_methods
invert_cholesky	(bool) Flag for Cholesky inversion method.
invert_lu	(bool) Flag for LU inversion method.
invert_univariate	(bool) Flag for univariate inversion method (recommended).
memory_conserve	(bool) Flag to conserve the maximum amount of memory.
memory_no_filtered	(bool) Flag to prevent storing filtered state and covariance matrices.
memory_no_filtered_cov	(bool) Flag to prevent storing filtered state covariance matrices.
memory_no_filtered_mean	(bool) Flag to prevent storing filtered states.
memory_no_forecast	(bool) Flag to prevent storing all forecast-related output.
memory_no_forecast_cov	(bool) Flag to prevent storing forecast error covariance matrices.
memory_no_forecast_mean	(bool) Flag to prevent storing forecasts and forecast errors.
memory_no_gain	(bool) Flag to prevent storing the Kalman gain matrices.
memory_no_likelihood	(bool) Flag to prevent storing likelihood values for each observation.
memory_no_predicted	(bool) Flag to prevent storing predicted state and covariance matrices.
memory_no_predicted_cov	(bool) Flag to prevent storing predicted state covariance matrices.
memory_no_predicted_mean	(bool) Flag to prevent storing predicted states.
memory_no_smoothing	(bool) Flag to prevent storing likelihood values for each observation.
memory_no_std_forecast	(bool) Flag to prevent storing standardized forecast errors.
memory_options
memory_store_all	(bool) Flag for storing all intermediate results in memory (default).
obs	(array) Observation vector: \(y~(k\_endog \times nobs)\)
obs_cov	(array) Observation covariance matrix: \(H~(k\_endog \times k\_endog \times nobs)\)
obs_intercept	(array) Observation intercept: \(d~(k\_endog \times nobs)\)
prefix	(str) BLAS prefix of currently active representation matrices
selection	(array) Selection matrix: \(R~(k\_states \times k\_posdef \times nobs)\)
smooth_alternative	(bool) Flag for alternative (modified Bryson-Frazier) smoothing.
smooth_classical	(bool) Flag for classical (see e.g.
smooth_conventional	(bool) Flag for conventional (Durbin and Koopman, 2012) Kalman smoothing.
smooth_method
smooth_methods
smooth_univariate	(bool) Flag for univariate smoothing (uses modified Bryson-Frazier timing).
smoother_all
smoother_disturbance
smoother_disturbance_cov
smoother_output
smoother_outputs
smoother_state
smoother_state_autocov
smoother_state_cov
solve_cholesky	(bool) Flag for Cholesky and linear solver inversion method (recommended).
solve_lu	(bool) Flag for LU and linear solver inversion method.
stability_force_symmetry	(bool) Flag for enforcing covariance matrix symmetry
stability_method	(int) Stability method bitmask.
stability_methods
state_cov	(array) State covariance matrix: \(Q~(k\_posdef \times k\_posdef \times nobs)\)
state_intercept	(array) State intercept: \(c~(k\_states \times nobs)\)
time_invariant	(bool) Whether or not currently active representation matrices are time-invariant
timing_init_filtered	(bool) Flag for the alternate timing convention (Kim and Nelson, 2012).
timing_init_predicted	(bool) Flag for the default timing convention (Durbin and Koopman, 2012).
timing_options
transition	(array) Transition matrix: \(T~(k\_states \times k\_states \times nobs)\)