Data Generating Processes

Abstract

Before we attempt to build models for some data series, we need to describe the scope of coverage, i.e., the class of data generating processes for which we design model-building algorithms. First, we assume that data are generated by linear processes. Second, throughout most of the book, we further assume that the processes are at least covariance (or weakly) stationary. We assume, that is, that the mean of the process is a constant not varying with time, and that the covariance matrices are functions of the differences of the two time instants and not of these two instants themselves. Later, when we discuss series with apparent trends, we drop this constant-mean assumption. Third, the spectral density matrix of the processes are rational—i.e., the elements of the matrix are ratios of finite order polynomials. This last assumption means that we can use a finite number of parameters to describe the process, such as finite-order ARMA processes or finite-dimensional state space models which are discussed in Chapter 4.