Time Series

Introduction to

Time Series Analysis and Forecasting

with Applications of SAS and SPSS

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Introduction to

Time Series Analysis and Forecasting

with Applications of SAS and SPSS

Robert A. Yaffee

Statistics and Social Science Group Academic Computing Service of the Information Technology Services New York University New York, New York and Division of Geriatric Psychiatry State University of New York Health Science Center at Brooklyn Brooklyn, NY with

Monnie McGee

Hunter College City University of New York New York, New York

ACADEMIC PRESS, INC.

San Diego London Boston New York Sydney Tokyo Toronto

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For Liz and Mike

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Contents

Preface xv

Chapter 1

Introduction and Overview

1.1. 1.2. 1.3. 1.4. 1.5. 1.6. 1.7. 1.8. 1.9. 1.10. 1.11. Purpose Time Series Missing Data Sample Size Representativeness Scope of Application Stochastic and Deterministic Processes Stationarity Methodological Approaches Importance Notation 1.11.1. Gender 1.11.2. Summation 1.11.3. Expectation 1.11.4. Lag Operator 1.11.5. The Difference Operator 1.11.6. Mean-Centering the Series References 1 2 3 3 4 4 5 5 7 9 9 9 10 11 12 12 12 13

Chapter 2

Extrapolative and Decomposition Models

2.1. Introduction 15

vii

viii

Contents

2.2. Goodness-of-Fit Indicators 2.3. Averaging Techniques 2.3.1. The Simple Average 2.3.2. The Single Moving Average 2.3.3. Centered Moving Averages 2.3.4. Double Moving Averages 2.3.5. Weighted Moving Averages 2.4. Exponential Smoothing 2.4.1. Simple Exponential Smoothing 2.4.2. Holt’s Linear Exponential Smoothing 2.4.3. The Dampened Trend Linear Exponential Smoothing Model 2.4.4. Exponential Smoothing for Series with Trend and Seasonality: Winter’s Methods 2.4.5. Basic Evaluation of Exponential Smoothing 2.5. Decomposition Methods 2.5.1. Components of a Series 2.5.2. Trends 2.5.3. Seasonality 2.5.4. Cycles 2.5.5. Background 2.5.6....