Stationary time series models

In this section, we will describe a few stationary time series models. As we will see, these can be used to model a number of real-world processes.

Moving average models

A moving average (MA) process is a stochastic process in which the random variable at time step t is a linear combination of the most recent (in time) terms of a white noise process. Concretely, we can write this in an equation as follows:

In the previous equation, and henceforth, we will assume that the e terms are white noise random variables with mean 0 and variance σ_w². We can describe a moving average process in an equivalent way by making use of the backshift operator, B. The backshift operator is an operator that when applied to a random variable in a stochastic process at time t, produces the random variable at the previous time step, t-1. For example:

We can obtain random variables further back in time by successive applications of the backshift operator. B², for example, indicates the...