statsmodels.tsa.statespace.representation.Representation.initialize_components¶
- Representation.initialize_components(a=None, Pstar=None, Pinf=None, A=None, R0=None, Q0=None)[source]¶
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.
- aarray_like,
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.