Appendix B: Inherited attributes and methods¶
sm.tsa.statespace.MLEModel¶
The methods available to all classes inheriting from the base classes
sm.tsa.statespace.MLEModel are listed in
Table 7 and the attributes are listed in
Table 8.
| Method | Description |
|---|---|
filter |
Kalman filtering |
fit |
Fits the model by maximum likelihood via Kalman filter. |
loglike |
Joint loglikelihood evaluation |
loglikeobs |
Loglikelihood evaluation |
set_filter_method |
Set the filtering method |
set_inversion_method |
Set the inversion method |
set_stability_method |
Set the numerical stability method |
set_conserve_memory |
Set the memory conservation method |
set_smoother_output |
Set the smoother output |
simulation_smoother |
Retrieve a simulation smoother for the statespace model. |
initialize_known |
Initialize the Kalman filter with known values |
initialize_approximate_diffuse |
Specify approximate diffuse Kalman filter initialization |
initialize_stationary |
Initialize the statespace model as stationary |
simulate |
Simulate a new time series following the state space model |
impulse_responses |
Impulse response function |
| Attribute | Description |
|---|---|
endog |
The observed (endogenous) dataset |
exog |
The dataset of explanatory variables (if applicable) |
start_params |
Parameter vector used to initialize parameter estimation iterations |
param_names |
Human-readable names of parameters |
initialization |
The selected method for Kalman filter initialization |
initial_variance |
The initial variance to use in approximate diffuse initialization |
loglikelihood_burn |
The number of observations during which the likelihood is not evaluated |
tolerance |
The tolerance at which the Kalman filter determines convergence to steady-state |
| Attribute | Description |
|---|---|
'obs_intercept' |
Observation intercept; \(d_t\) |
'design' |
Design matrix; \(Z_t\) |
'obs_cov' |
Observation disturbance covariance matrix; \(H_t\) |
'state_intercept' |
State intercept; \(c_t\) |
'transition' |
Transition matrix; \(T_t\) |
'selection' |
Selection matrix; \(R_t\) |
'state_cov' |
State disturbance covariance matrix; \(Q_t\) |
The fit, filter, and smooth methods return a
sm.tsa.statespace.MLEResults object; its methods and attributes are given
below.
The simulation_smoother method returns a SimulationSmoothResults
object; its methods and attributes are also given below.
sm.tsa.statespace.MLEResults¶
The methods available to these results objects are listed in Table 10 and the attributes are listed in Table 11.
| Method | Description |
|---|---|
test_normality |
Jarque-Bera for normality of standardized residuals. |
test_heteroskedasticity |
Test for heteroskedasticity (break in the variance) of standardized residuals |
test_serial_correlation |
Ljung-box test for no serial correlation of standardized residuals |
get_prediction |
In-sample prediction and out-of-sample forecasting; returns all prediction results |
get_forecast |
Out-of-sample forecasts; returns all forecasting results |
predict |
In-sample prediction and out-of-sample forecasting; only returns predicted values |
forecast |
Out-of-sample forecasts; only returns forecasted values |
simulate |
Simulate a new time series following the state space model |
impulse_responses |
Impulse response function |
plot_diagnostics |
Diagnostic plots for standardized residuals of one endogenous variable |
summary |
Summarize the results |
| Attribute | Description |
|---|---|
aic |
Akaike Information Criterion |
bic |
Bayes Information Criterion |
bse |
Standard errors of fitted parameters |
conf_int |
Returns the confidence interval of the fitted parameters |
cov_params_default |
Covariance matrix of fitted parameters |
filtered_state |
Filtered state mean; \(a_{t|t}\) |
filtered_state_cov |
Filtered state covariance matrix; \(P_{t|t}\) |
fittedvalues |
Fitted values of the model; alias for forecasts. |
forecasts |
Forecasts; \(\hat y_t = Z_t a_t\) |
forecasts_error |
Forecast errors; \(v_t\) |
forecasts_error_cov |
Forecast error covariance matrix; \(F_t\) |
hqic |
Hannan-Quinn Information Criterion |
kalman_gain |
Kalman gain; \(K_t\) |
llf_obs |
The values of the loglikelihood function at the fitted parameters; \(\log L(y_t)\) |
llf |
The value of the joint loglikelihood function at the fitted parameters; \(\log L(Y_n)\) |
loglikelihood_burn |
The number of observations during which the likelihood is not evaluated |
nobs |
The number of observations in the dataset |
params |
The fitted parameters |
predicted_state |
Predicted state mean; \(a_t\) |
predicted_state_cov |
Predicted state covariance matrix; \(P_t\) |
pvalues |
The p-values associated with the z-statistics of the coefficients |
resid |
Residuals of the model; alias for forecasts_errors |
smoothed_measurement_disturbance |
Smoothed observation disturbance mean; \(\hat \varepsilon_t\) |
smoothed_measurement_disturbance_cov |
Smoothed observation disturbance covariance matrix; \(Var(\varepsilon_t \mid Y_n)\) |
smoothed_state |
Smoothed state mean; \(\hat \alpha_t\) |
smoothed_state_cov |
Smoothed state covariance matrix; \(V_t\) |
smoothed_state_disturbance |
Smoothed state disturbance mean; \(\hat \eta_t\) |
smoothed_state_disturbance_cov |
Smoothed state disturbance covariance matrix; \(Var(\eta_t \mid Y_n)\) |
zvalues |
The z-values of the standard errors of fitted parameters |
SimulationSmoothResults¶
The only method of a SimulationSmoothResults object is given in
Table 12. After this method is called, the
attributes in Table 13 are populated. Each time
the method is called, these attributes change to the newly simulated values.
| Method | Description |
|---|---|
simulate |
Perform simulation smoothing |
| Attribute | Description |
|---|---|
simulated_state |
Simulated state vector; \(\tilde \alpha_t\) |
simulated_measurement_disturbance |
Simulated measurment disturbance; \(\tilde \varepsilon_t\) |
simulated_state_disturbance |
Simulated state disturbance; \(\tilde \eta_t\) |