## Chapter 2: Simple Models: Autoregression

2.1.1 Terminology and Notation

2.2.1 PROC ARIMA for Forecasting

2.2.2 Backshift Notation *B* for Time Series

2.2.3 Yule-Walker Equations for Covariances

2.3 Fitting an AR Model in PROC REG

### 2.1 Introduction

A simple and yet quite useful model, the order 1 autoregressive, AR(1), model is used in this chapter to introduce some of the basic ideas in time series analysis and forecasting.

### 2.1.1 Terminology and Notation

Often, you can forecast series *Y*_{t} simply based on past values *Y*_{t}_{–1}, *Y*_{t}_{–2}, …. For example, suppose *Y*_{t} satisfies the following:

$${Y}_{t}-\mu =\rho \left({Y}_{t-1}-\mu \right)+{e}_{t}\left(2\text{.}1\right)$$

where *e*_{t} is a sequence of uncorrelated *N*(0, σ^{2}) variables. The term for such an

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