State-Space Models, Kalman Filtering, and Related Topics

Abstract

In this chapter we present and discuss the state-variable (state-space) model and its basic properties. The Kalman filtering and smoothing procedures associated with state-space models will be developed. The relation of time-invariant state-variable models to vector ARMA models, including the state-space representations for vector ARMA models, and the associated topics of minimal dimensionality of the state vector and the relation with Kronecker indices and McMillan degree of a process will also be discussed. The use of the state-space formulation for construction of the exact likelihood function for the vector ARMA model will be presented also. In addition, discussion of results for the classical approach to smoothing and filtering of time series will be presented.