statsmodels.tsa.statespace.initialization.Initialization.from_components#
- classmethod Initialization.from_components(k_states, a=None, Pstar=None, Pinf=None, A=None, R0=None, Q0=None)[source]#
Construct initialization object from component matrices
- Parameters:
- k_states
int Number of states in the time series process.
- 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.
- k_states
- Returns:
initializationInitialization object.
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