statsmodels.tsa.statespace.representation.Representation¶
-
class
statsmodels.tsa.statespace.representation.
Representation
(k_endog, k_states, k_posdef=None, initial_variance=1000000.0, nobs=0, dtype=<type 'numpy.float64'>, design=None, obs_intercept=None, obs_cov=None, transition=None, state_intercept=None, selection=None, state_cov=None, **kwargs)[source]¶ State space representation of a time series process
Parameters: k_endog : array_like or integer
The observed time-series process y if array like or the number of variables in the process if an integer.
k_states : int
The dimension of the unobserved state process.
k_posdef : int, 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.
initial_variance : float, optional
Initial variance used when approximate diffuse initialization is specified. Default is 1e6.
initialization : {‘approximate_diffuse’,’stationary’,’known’}, optional
Initialization method for the initial state.
initial_state : array_like, optional
If known initialization is used, the mean of the initial state’s distribution.
initial_state_cov : array_like, optional
If known initialization is used, the covariance matrix of the initial state’s distribution.
nobs : integer, optional
If an endogenous vector is not given (i.e. k_endog is an integer), the number of observations can optionally be specified. If not specified, they will be set to zero until data is bound to the model.
dtype : dtype, optional
If an endogenous vector is not given (i.e. k_endog is an integer), the default datatype of the state space matrices can optionally be specified. Default is np.float64.
design : array_like, optional
The design matrix, Z. Default is set to zeros.
obs_intercept : array_like, optional
The intercept for the observation equation, d. Default is set to zeros.
obs_cov : array_like, optional
The covariance matrix for the observation equation H. Default is set to zeros.
transition : array_like, optional
The transition matrix, T. Default is set to zeros.
state_intercept : array_like, optional
The intercept for the transition equation, c. Default is set to zeros.
selection : array_like, optional
The selection matrix, R. Default is set to zeros.
state_cov : array_like, optional
The covariance matrix for the state equation Q. Default is set to zeros.
**kwargs :
Additional keyword arguments. Not used directly. It is present to improve compatibility with subclasses, so that they can use **kwargs to specify any default state space matrices (e.g. design) without having to clean out any other keyword arguments they might have been passed.
Notes
A general state space model is of the form
y_t & = Z_t \alpha_t + d_t + \varepsilon_t \\ \alpha_t & = T_t \alpha_{t-1} + c_t + R_t \eta_t \\
where y_t refers to the observation vector at time t, \alpha_t refers to the (unobserved) state vector at time t, and where the irregular components are defined as
\varepsilon_t \sim N(0, H_t) \\ \eta_t \sim N(0, Q_t) \\
The remaining variables (Z_t, d_t, H_t, T_t, c_t, R_t, Q_t) in the equations are matrices describing the process. Their variable names and dimensions are as follows
Z : design (k\_endog \times k\_states \times nobs)
d : obs_intercept (k\_endog \times nobs)
H : obs_cov (k\_endog \times k\_endog \times nobs)
T : transition (k\_states \times k\_states \times nobs)
c : state_intercept (k\_states \times nobs)
R : selection (k\_states \times k\_posdef \times nobs)
Q : state_cov (k\_posdef \times k\_posdef \times nobs)
In the case that one of the matrices is time-invariant (so that, for example, Z_t = Z_{t+1} ~ \forall ~ t), its last dimension may be of size 1 rather than size nobs.
References
[R27] Durbin, James, and Siem Jan Koopman. 2012. Time Series Analysis by State Space Methods: Second Edition. Oxford University Press. Attributes
nobs int The number of observations. k_endog int The dimension of the observation series. k_states int The dimension of the unobserved state process. k_posdef int The dimension of a guaranteed positive definite covariance matrix describing the shocks in the measurement equation. shapes dictionary of name:tuple A dictionary recording the initial shapes of each of the representation matrices as tuples. initialization str Kalman filter initialization method. Default is unset. initial_variance float Initial variance for approximate diffuse initialization. Default is 1e6. Methods
bind
(endog)Bind data to the statespace representation initialize_approximate_diffuse
([variance])Initialize the statespace model with approximate diffuse values. initialize_known
(initial_state, ...)Initialize the statespace model with known distribution for initial state. initialize_stationary
()Initialize the statespace model as stationary. Attributes
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. obs
(array) Observation vector: y~(k\_endog \times nobs) obs_cov
(array) Observation covariance matrix: 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) 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 transition
(array) Transition matrix: T~(k\_states \times k\_states \times nobs)