class statsmodels.regression.recursive_ls.RecursiveLS(endog, exog, **kwargs)[source]

Recursive least squares

  • endog (array_like) – The observed time-series process \(y\)
  • exog (array_like) – Array of exogenous regressors, shaped nobs x k.


Recursive least squares (RLS) corresponds to expanding window ordinary least squares (OLS).

This model applies the Kalman filter to compute recursive estimates of the coefficients and recursive residuals.


[*]Durbin, James, and Siem Jan Koopman. 2012. Time Series Analysis by State Space Methods: Second Edition. Oxford University Press.


filter([return_ssm]) Kalman filtering
fit() Fits the model by application of the Kalman filter
from_formula(formula, data[, subset]) Not implemented for state space models
hessian(params, *args, **kwargs) Hessian matrix of the likelihood function, evaluated at the given parameters
impulse_responses(params[, steps, impulse, …]) Impulse response function
information(params) Fisher information matrix of model
initialize() Initialize (possibly re-initialize) a Model instance.
initialize_known(initial_state, …)
initialize_statespace(**kwargs) Initialize the state space representation
loglike(params, *args, **kwargs) Loglikelihood evaluation
loglikeobs(params[, transformed, complex_step]) Loglikelihood evaluation
observed_information_matrix(params[, …]) Observed information matrix
opg_information_matrix(params[, …]) Outer product of gradients information matrix
predict(params[, exog]) After a model has been fit predict returns the fitted values.
prepare_data() Prepare data for use in the state space representation
score(params, *args, **kwargs) Compute the score function at params.
score_obs(params[, method, transformed, …]) Compute the score per observation, evaluated at params
set_conserve_memory([conserve_memory]) Set the memory conservation method
set_filter_method([filter_method]) Set the filtering method
set_inversion_method([inversion_method]) Set the inversion method
set_smoother_output([smoother_output]) Set the smoother output
set_stability_method([stability_method]) Set the numerical stability method
simulate(params, nsimulations[, …]) Simulate a new time series following the state space model
simulation_smoother([simulation_output]) Retrieve a simulation smoother for the state space model.
smooth([return_ssm]) Kalman smoothing
transform_jacobian(unconstrained[, …]) Jacobian matrix for the parameter transformation function
transform_params(unconstrained) Transform unconstrained parameters used by the optimizer to constrained parameters used in likelihood evaluation
untransform_params(constrained) Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer
update(params, **kwargs) Update the parameters of the model


endog_names Names of endogenous variables
param_names (list of str) List of human readable parameter names (for parameters actually included in the model).
start_params (array) Starting parameters for maximum likelihood estimation.