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=<class '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

[R79]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.

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)