ABSTRACT
This chapter presents the main state estimation algorithms which are known as “filtering” and “fixed-interval smoothing.” Both focus on estimating the sequence of states, but are based on different information sets, and constitute the foundation of most state-space (SS) procedures. Kalman filter is used to compute the innovations required to evaluate the likelihood for an SS model, while smoothing algorithms are applied to estimate unobserved components in structural time-series models and to deal with samples containing missing values or aggregated data. The chapter discusses decomposition of smoothed moments and provides an example that illustrates the use of the smoothing algorithm to filter out the observational noise from a variable in an error-in-variables model.
