Further Topics

Abstract

In this final chapter we touch on a variety of topics of special interest The Kaiman recursions have had a profound impact in time series analysis and in many related areas. In Section 12.1 the basic recursions are derived and applied to ARMA processes with observational noise. A similar analysis is used in Sections 12.3 and 12.7 to deal with data having unequally spaced (or missing) values. In Section 12.2 we consider transfer function models, designed to exploit, for predictive purposes, the relationship between two time series when one leads the other. Section 12.4 deals with long-memory models, characterized by very slow convergence to zero of the autocorrelations ρ(h) as h → ∞. Such models are suggested by numerous observed series in hydrology and economics. In Section 12.5 we examine linear time-series models with infinite variance and in Section 12.6 we briefly consider non-linear models and their applications.