Further Topics

Abstract

In this chapter we touch on a variety of topics of special interest. In Section 11.1 we consider transfer function models, designed to exploit for predictive purposes the relationship between two time series when one acts as a leading indicator for the other. Section 11.2 deals with intervention analysis, which allows for possible changes in the mechanism generating a time series, causing it to have different properties over different time intervals. In Section 11.3 we introduce the very fast growing area of nonlinear time series analysis, and in Section 11.4 we discuss fractionally integrated ARMA processes, sometimes called “long-memory” processes on account of the slow rate of convergence of their autocorrelation functions to zero as the lag increases. In Section 11.5 we discuss continuous-time ARMA processes which, for continuously evolving processes, play a role analogous to that of ARMA processes in discrete time. Besides being of interest in their own right, they have proved a useful class of models in the representation of financial time series and in the modeling of irregularly spaced data.