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, statespace_classes=None, **kwargs)
[source]
State space representation of a time series process
Parameters: |
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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.
A general state space model is of the form
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
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
.
[*] | Durbin, James, and Siem Jan Koopman. 2012. Time Series Analysis by State Space Methods: Second Edition. Oxford University Press. |
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. |
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 – \(H~(k\_endog \times k\_endog \times nobs)\) |
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 time-invariant |
transition | (array) Transition matrix – \(T~(k\_states \times k\_states \times nobs)\) |
© 2009–2012 Statsmodels Developers
© 2006–2008 Scipy Developers
© 2006 Jonathan E. Taylor
Licensed under the 3-clause BSD License.
http://www.statsmodels.org/stable/generated/statsmodels.tsa.statespace.representation.Representation.html