ABSTRACT
Various models used in time series analysis can be treated uniformly within the state-space model framework. Many problems of time series analysis can be formulated as the state estimation of a state-space model. This chapter presents the Kalman filter algorithm and the smoothing algorithm for efficient state estimation. In addition, applications to the long-term prediction, interpolation and parameter estimation of a time series are also addressed. Therefore, to solve the state estimation problem for the state-space model, it is sufficient to obtain the mean vectors and the variance covariance matrices of the conditional distributions. However, for the state-space model, a very computationally efficient procedure for obtaining the joint conditional distribution of the state has been developed by means of a recursive computational algorithm.
