Moving Average Processes (MA)

Linear models for time series are the focus of this course. A time series $y_t$ follows a linear model if it can be represented as a linear combination of past realizations of a white noise process. This definition is quite broad, though. We use it as an umbrella term to encompass different types of models. In this lesson, we will study one of the most basic: the moving average.

Definition

A moving average (MA) is a type of linear time series model that uses a weighted average of random shocks at different time steps to calculate the present value of the series. These shocks are white noise. The term “moving” refers to the calculation moving along with the series, using the most recent set of shocks to forecast the current value of $y_t$.

We can denote a MA model as:

We can rewrite this equation more compactly:

Let’s break down this equation into its main components:

• $c$ is a constant.

• $\epsilon_t$ is white noise, with mean $0$ and variance $\sigma^2$.

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