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Forecasting with Dynamic Regression Models PDF

402 Pages·1991·10.775 MB·English
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Forecasting with Dynamic Regression Models Forecasting with Dynamic Regression Models ALAN PANKRATZ DePauw University Greencastle, Indiana Wiley-Interscience Publication JOHN WILEY & SONS INC. New York • Chichester • Brisbane • Toronto • Singapore A NOTE TO THE READER This book has been electronically reproduced from digital information stored at John Wiley & Sons, Inc. We are pleased that the use of this new technology will enable us to keep works of enduring scholarly value in print as long as there is a reasonable demand for them. The content of this book is identical to previous printings. In recognition of the importance of preserving what has been written, it is a policy of John Wiley & Sons, Inc., to have books of enduring value published in the United States printed on acid-free paper, and we exert our best efforts to that end. Copyright © 1991 by John Wiley & Sons, Inc. All rights reserved. Published simultaneously in Canada. Reproduction or translation of any part of this work beyond that permitted by Section 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. Requests for permission or further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. Library of Congress Cataloging in Publication Data: Pankratz, Alan, 1944- Forecasting with dynamic regression models / Alan Pankratz. p. cm. — (Wiley series in probability and mathematical statistics. Applied probability and statistics, ISSN 0271-6356) "A Wiley-Interscience publication." Includes bibliographical references and index. ISBN 0-471-61528-5 1. Time-series analysis. 2. Regression analysis. 3. Prediction theory. I. Title. II. Series. QA280.P368 1991 519.5'5-dc20 91-12484 CIP 10 9 8 7 6 5 To Aaron Mark Dietrich and Sherith Hope Laura Contents Preface Chapter 1 Introduction and Overview 1.1 Related Time Series, 1 1.2 Overview: Dynamic Regression Models, 7 1.3 Box and Jenkins' Modeling Strategy, 15 1.4 Correlation, 17 1.5 Layout of the Book, 21 Questions and Problems, 22 Chapter 2 A Primer on ARIMA Models 2.1 Introduction, 24 2.2 Stationary Variance and Mean, 27 2.3 Autocorrelation, 34 2.4 Five Stationary ARIMA Processes, 39 2.5 ARIMA Modeling in Practice, 49 2.6 Backshift Notation, 52 2.7 Seasonal Models, 54 2.8 Combined Nonseasonal and Seasonal Processes, 57 2.9 Forecasting, 59 2.10 Extended Autocorrelation Function, 62 2.11 Interpreting ARIMA Model Forecasts, 64 Questions and Problems, 69 viii CONTENTS Case 1 Federal Government Receipts (ARIMA) 72 Chapter 3 A Primer on Regression Models 82 3.1 Two Types of Data, 82 3.2 The Population Regression Function (PRF) with One Input, 82 3.3 The Sample Regression Function (SRF) with One Input, 86 3.4 Properties of the Least-Squares Estimators, 88 3.5 Goodness of Fit (R2), 89 3.6 Statistical Inference, 92 3.7 Multiple Regression, 93 3.8 Selected Issues in Regression, 96 3.9 Application to Time Series Data, 103 Questions and Problems, 113 Case 2 Federal Government Receipts (Dynamic Regression) 115 Case 3 Kilowatt-Hours Used 131 Chapter 4 Rational Distributed Lag Models 147 4.1 Linear Distributed Lag Transfer Functions, 148 4.2 A Special Case: The Koyck Model, 150 4.3 Rational Distributed Lags, 156 4.4 The Complete Rational Form DR Model and Some Special Cases, 163 Questions and Problems, 165 Chapter 5 Building Dynamic Regression Models: Model Identification 167 5.1 Overview, 167 5.2 Preliminary Modeling Steps, 168 5.3 The Linear Transfer Function (LTF) Identification Method, 173 5.4 Rules for Identifying Rational Distributed Lag Transfer Functions, 184 Questions and Problems, 193 Appendix 5A The Corner Table, 194 Appendix 5B Transfer Function Identification Using Prewhitening and Cross Correlations, 197 CONTENTS ix Chapter 6 Building Dynamic Regression Models: Model Checking, Reformulation, and Evaluation 202 6.1 Diagnostic Checking and Model Reformulation, 202 6.2 Evaluating Estimation Stage Results, 209 Questions and Problems, 215 Case 4 Housing Starts and Sales 217 Case 5 Industrial Production, Stock Prices, and Vendor Performance 232 Chapter 7 Intervention Analysis 253 7.1 Introduction, 253 7.2 Pulse Interventions, 254 7.3 Step Interventions, 259 7.4 Building Intervention Models, 264 7.5 Multiple and Compound Interventions, 272 Questions and Problems, 276 Case 6 Year-End Loading 279 Chapter 8 Intervention and Outlier Detection and Treatment 290 8.1 The Rationale for Intervention and Outlier Detection, 291 8.2 Models for Intervention and Outlier Detection, 292 8.3 Likelihood Ratio Criteria, 299 8.4 An Iterative Detection Procedure, 313 8.5 Application, 315 8.6 Detected Events Near the End of a Series, 319 Questions and Problems, 320 Appendix 8A BASIC Program to Detect AO, LS, and IO Events, 321 Appendix 8B Specifying IO Events in the SCA System, 322 Chapter 9 Estimation and Forecasting 324 9.1 DR Model Estimation, 324 9.2 Forecasting, 328 Questions and Problems, 340 Appendix 9A A BASIC Routine for Computing the Nonbiasing Factor in (9.2.24), 340 X CONTENTS Chapter 10 Dynamic Regression Models in a Vector ARMA Framework 342 10.1 Vector ARMA Processes, 342 10.2 The Vector AR (IT Weight) Form, 345 10.3 DR Models in VAR Form, 346 10.4 Feedback Check, 349 10.5 Check for Contemporaneous Relationship and Dead Time, 354 Questions and Problems, 356 Appendix 357 Table A Student's / Distribution, 357 Table B x2 Critical Points, 359 Table C F Critical Points, 360 Data Appendix 362 References 376 Index 381 Preface Single-equation regression models are one of the most widely used statistical forecasting tools. Over the last two decades many ideas relevant to regression forecasting have arisen in the time series literature, starting with the first edition of Box and Jenkins' text, Time Series Analysis: Forecasting and Control, Holden-Day (1976). Those who apply regression methods to time series data without knowledge of these ideas may miss out on a better understanding of their data, better models, and better forecasts. This book is a companion volume to my earlier text, Forecasting with Univariate Box-Jenkins Models: Concepts and Cases, Wiley (1983), where I present the Box-Jenkins modeling strategy as applied to ARIMA models. There is more to Box and Jenkins than ARIMA models. They also discuss "combined transfer function-disturbance" models, or what I call dynamic regression models. The purpose of the present text is to pull together recent time series ideas in the Box-Jenkins tradition that are important for the informed practice of single-equation regression forecasting. I pay special attention to possible intertemporal (dynamic) patterns —distributed lag re- sponses of the output series (dependent variable) to the input series (indepen- dent variables), and the autocorrelation patterns of the regression disturb- ance. This book may be used as a main text for undergraduate and beginning graduate courses in applied time series and forecasting in areas such as economics, business, biology, political science, engineering, statistics, and decision science. It may be used in advanced courses to supplement theoreti- cal readings with applications. And it can serve as a guide to the construction and use of regression forecasting models for practicing forecasters in business and government. Special features of this book include the following: • Many step-by-step examples using real data, including cases with multiple inputs, both stochastic and deterministic. • Emphasis on model interpretation. xi xii PREFACE • Emphasis on a model identification method that is easily applied with multiple inputs. ■ Suggested practical rules for identifying rational form transfer functions. • Emphasis on feedback checks as a preliminary modeling step. • Careful development of an outlier and intervention detection method, including a BASIC computing routine. • A chapter linking dynamic regression models to vector ARMA models. • Use of the extended autocorrelation function to identify ARIMA models. While there are other books that cover some of these ideas, they tend to cover them briefly, or at a fairly high level of abstraction, or with few supporting applications. I present the theory at a low level, and I show how these ideas may be applied to real data by means of six case studies, along with other examples within the chapters. Several additional data sets are provided in the Data Appendix. The examples and cases are drawn mainly from economics and business, but the ideas illustrated are also applicable to data from other disciplines. Those who read the entire text will notice some repetition; I realize that many readers will read only selected chapters and cases, and that most won't already know the contents of this book before they read, so I have tried to repeat some key ideas. I hope my readers will learn enough of the main ideas and practices of dynamic regression forecasting to feel more comfortable and be more insightful when doing their own data analysis, criticizing their own procedures and results, moving ahead to more advanced literature and pract- ices, and when moving back to less advanced methods. I have successfully used a majority of the material in this book with undergraduates, most of whom have had just one course in statistics. I assume that readers have been exposed to the rudiments of probability, hypothesis testing, and interval estimation. A background in regression meth- ods is helpful but not required; Chapter 3 is an introduction to the fundamen- tals of regression. I use matrix algebra in a few places, primarily Chapter 10, but a knowledge of matrix algebra is not required to understand the main ideas in the text. For many readers the most difficult part of the text may be the use of backshift notation. If you are one of those readers, to you I say (1) it's only notation, (2) learning to use it is easier than learning to ride a bicycle, and (3) it's immensely useful. As you read this book, I hope you find parts that are interesting, informa- tive, and helpful. When you do, you should be as grateful as I am to Gregory Hudak, Brooks Elliott, and an anonymous reviewer who provided many excellent comments on a draft of the manuscript. I am also grateful to Fran Cappelletti for his perceptive comments on parts of the manuscript. I wish I could also blame shortcomings and undetected errors on these people, but I can't; I didn't take all of their advice, and any problems you encounter are my responsibility. Various members of the DePauw University Computer

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