CHAPTER 10 - STATISTICAL MODELS, II

Abstract

The sequences of random variables determined by a recursive relation are often encountered in applications {φn} and {ψn} being some sequences of functions and {Vn} a sequence of independent random variables with zero expectations. The relation determines a model generating the sequence {Yn} from the sequence of independent random variables {Vn}. Such models are called autoregression models. In the case where the functions φn are linear and are independent of Yn,……, Yn+p–1, equation determines a liner autoregression model. It is clear that linear autoregression models and moving average models represent special cases of a combined model. Apart from linear and nonlinear autoregression models, more general models are often encountered in practice, described by nonlinear difference equations. The problem of the estimation of the sequence of random vectors {Yn} determined by a difference equation of the nonlinear form by the results of a measurement of some functions of the vector Yn at every step is of great importance for practice. Thus, the problem arises of the estimation of the random vectors Yn determined by the difference equation using the results of observation of the random vectors.