In Chapter 22 it was argued that the respecification of the linear regression model induced by the inappropriateness of the independent sample assumption led to a new statistical model which we called the dynamic linear regression (DLR) model. The purpose of the present chapter is to consider the statistical analysis (specification, estimation, testing and prediction) of the DLR model.

The dependence in the sample raises the issue of introducing the concept of dependent random variables or stochastic processes. For this reason the reader is advised to refer back to Chapter 8 where the idea of a stochastic process and related concepts are discussed in some detail before proceeding further with the discussion which follows.

The linear regression model can be viewed as a statistical model derived by reduction from the joint distribution D(Z1 …, ZT; ψ), where, and {Zt,t∈T} is assumed to be a normal, independent and identically distributed (NIID) vector stochastic process. For the purposes of the present chapter we need to extend this to a more general stochastic process in order to take the dependence, which constitutes additional systematic information, into consideration.

In Chapter 21 the identically distributed component was relaxed leading to time varying parameters. The main aim of the present chapter is to relax the independence component but retain the identically distributed assumption in the form of stationarity.

In Section 23.1 the DLR is specified assuming that {Zt,t∈T} is a stationary, asymptotically independent normal process.