Probability Models for Time Series

Abstract

This chapter describes a variety of probability models for time series, which are collectively called stochastic processes. Most physical processes in the real world involve a random or stochastic element in their structure, and a stochastic process can be described as ‘a statistical phenomenon that evolves in time according to probabilistic laws’. Well-known examples are the length of a queue, the size of a bacterial colony, and the air temperature on successive days at a particular site. Many authors use the term ‘stochastic process’ to describe both the real physical process and a mathematical model of it. The word ‘stochastic’, which is of Greek origin, is used to mean ‘pertaining to chance’, and many writers use ‘random process’ as a synonym for stochastic process.