Vector Stochastic Processes

Abstract

In this chapter some notation is introduced and assumptions are discussed that will be used in later parts of the book. As explained in Chapter 1 the main concern of this study will be with forecasting economic variables of interest. Assuming that T observations x_kt, t = 1,…,T; k = 1,…,K; for each of the K time series variables x₁,…,x_k are available one possible approach is to construct a model for the generation process of the multiple time series x _t = (x_1t,…,x_kt)', t = 1,…T, and use that model for predicting future values of the variables x₁,…x_k. The model for the data generating process is chosen from the class of stochastic processes. In the following sections specific stochastic processes are introduced that are often suitable for modelling economic data. In Section 2.1 nondeterministic stationary processes are considered, in Section 2.2 an extension to certain types of nonstationary processes is provided and in Section 2.3 the special class of vector ARMA (autoregressive moving average) processes is discussed.