This chapter reviews the usefulness of the Kalman filter for parameter estimation and inference about unobserved variables in linear dynamic systems. Applications include exact maximum likelihood estimation of regressions with ARMA disturbances, time-varying parameters, missing observations, forming an inference about the public's expectations about inflation, and specification of business cycle dynamics. The chapter also reviews models of changes in regime and develops the parallel between such models and linear state-space models. The chapter concludes with a brief discussion of alternative approaches to nonlinear filtering.
