statsmodels.tsa.statespace.simulation_smoother.SimulationSmoother.initialize_components

SimulationSmoother.initialize_components(a=None, Pstar=None, Pinf=None, A=None, R0=None, Q0=None)

Initialize the statespace model with component matrices

Parameters
aarray_like, optional

Vector of constant values describing the mean of the stationary component of the initial state.

Pstararray_like, optional

Stationary component of the initial state covariance matrix. If given, should be a matrix shaped k_states x k_states. The submatrix associated with the diffuse states should contain zeros. Note that by definition, Pstar = R0 @ Q0 @ R0.T, so either R0,Q0 or Pstar may be given, but not both.

Pinfarray_like, optional

Diffuse component of the initial state covariance matrix. If given, should be a matrix shaped k_states x k_states with ones in the diagonal positions corresponding to states with diffuse initialization and zeros otherwise. Note that by definition, Pinf = A @ A.T, so either A or Pinf may be given, but not both.

Aarray_like, optional

Diffuse selection matrix, used in the definition of the diffuse initial state covariance matrix. If given, should be a k_states x k_diffuse_states matrix that contains the subset of the columns of the identity matrix that correspond to states with diffuse initialization. Note that by definition, Pinf = A @ A.T, so either A or Pinf may be given, but not both.

R0array_like, optional

Stationary selection matrix, used in the definition of the stationary initial state covariance matrix. If given, should be a k_states x k_nondiffuse_states matrix that contains the subset of the columns of the identity matrix that correspond to states with a non-diffuse initialization. Note that by definition, Pstar = R0 @ Q0 @ R0.T, so either R0,Q0 or Pstar may be given, but not both.

Q0array_like, optional

Covariance matrix associated with stationary initial states. If given, should be a matrix shaped k_nondiffuse_states x k_nondiffuse_states. Note that by definition, Pstar = R0 @ Q0 @ R0.T, so either R0,Q0 or Pstar may be given, but not both.

Notes

The matrices a, Pstar, Pinf, A, R0, Q0 and the process for initializing the state space model is as given in Chapter 5 of [1]. For the definitions of these matrices, see equation (5.2) and the subsequent discussion there.

References

1

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