SAS for Forecasting Time Series, Third Edition, 3rd Edition

Chapter 2: Simple Models: Autoregression

2.1 Introduction

2.1.1 Terminology and Notation

2.1.2 Statistical Background

2.2 Forecasting

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, σ²) variables. The term for such an