# 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.

Table 7 Methods available to subclasses of sm.tsa.statespace.MLEModel
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
Table 8 Attributes available to subclasses of sm.tsa.statespace.MLEModel
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
Table 9 Slice keys available to subclasses of sm.tsa.statespace.MLEModel
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.

Table 10 Methods available to results objects from fit, filter, and smooth
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
Table 11 Attributes available to results objects from fit, filter, and smooth
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.

Table 12 Methods available to results objects from simulation_smoother
Method Description
simulate Perform simulation smoothing
Table 13 Attributes available to results objects from simulation_smoother
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; $$\tilde \eta_t$$