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 Yt simply based on past values Yt–1, Yt–2, …. For example, suppose Yt satisfies the following:

Ytμ=ρ(Yt-1μ)+et   (2.1)

where et is a sequence of uncorrelated N(0, σ2) variables. The term for such an

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