Difference Equations and Stochastic Processes

Abstract

Stochastic processes are an integral part of all models examined in Parts I and II of this book. Linear difference equations, the building blocks of (vector) autoregressive stochastic processes, are reviewed in the first part of the chapter. Subsequently, Heer and Maußner formally introduce readers to stochastic processes in discrete time, before analyzing Markov chains and techniques used to approximate continuously valued autoregressive processes via finite-state Markov chains. The final part of the chapter considers time series filters, which can help to extract stochastic trends from nonstationary stochastic processes.