Some Practical Applications of the Simulation Smoother in State Space Modeling

After the well-known Kalman filter (KF) and Kalman smoother (KS) algorithms, the simulation smoother emerges as the next key algorithm for operationalizing a linear state space model (SSM) in SSM-based data analysis. The KF and KS are typically used for model fitting, forecasting, interpolation of the response variable, and the estimation and extrapolation of latent components in the model. The simulation smoother further enhances data analysis by enabling the drawing of random samples from the joint distribution of the latent states, conditioned on the observed data. This presentation will demonstrate how the simulation smoother can be applied to practical problems, such as obtaining global (as opposed to pointwise) confidence bands for the latent components in an SSM (e.g., global confidence band for the latent level of a series) and deriving the sampling distribution of a function of the response variable forecasts.