Forecasting With Dynamic Regression Models

One of the most widely used tools in statistical forecasting, single equation regression models is examined here. A companion to the author's earlier work, Forecasting with Univariate Box-Jenkins Models: Concepts and Cases, the present text pulls together recent time series ideas and gives special attention to possible intertemporal patterns, distributed lag responses of output to input series and the auto correlation patterns of regression disturbance. It also includes six case studies.

Alan Pankratz is the author of Forecasting with Dynamic Regression Models, published by Wiley.

Preface

xi

Introduction and Overview

1

(23)

Related Time Series

1

(6)

Overview: Dynamic Regression Models

7

(8)

Box and Jenkins' Modeling Strategy

15

(2)

Correlation

17

(4)

Layout of the Book

21

(3)

Questions and Problems

22

(2)

A Primer on ARIMA Models

24

(58)

Introduction

24

(3)

Stationary Variance and Mean

27

(7)

Autocorrelation

34

(5)

Five Stationary ARIMA Processes

39

(10)

ARIMA Modeling in Practice

49

(3)

Backshift Notation

52

(2)

Seasonal Models

54

(3)

Combined Nonseasonal and Seasonal Processes

57

(2)

Forecasting

59

(3)

Extended Autocorrelation Function

62

(2)

Interpreting ARIMA Model Forecasts

64

(18)

Questions and Problems

69

(3)

Federal Government Receipts (ARIMA)

72

(10)

A Primer on Regression Models

82

(65)

Two Types of Data

82

(1)

The Population Regression Function (PRF) with One Input

82

(4)

The Sample Regression Function (SRF) with One Input

86

(2)

Properties of the Least-Squares Estimators

88

(1)

Goodness of Fit (R2)

89

(3)

Statistical Inference

92

(1)

Multiple Regression

93

(3)

Selected Issues in Regression

96

(7)

Application to Time Series Data

103

(44)

Questions and Problems

113

(2)

Federal Government Receipts (Dynamic Regression)

115

(16)

Kilowatt-Hours Used

131

(16)

Rational Distributed Lag Models

147

(20)

Linear Distributed Lag Transfer Functions

148

(2)

A Special Case: The Koyck Model

150

(6)

Rational Distributed Lags

156

(7)

The Complete Rational Form DR Model and Some Special Cases

163

(4)

Questions and Problems

165

(2)

Building Dynamic Regression Models: Model Identification

167

(35)

Overview

167

(1)

Preliminary Modeling Steps

168

(5)

The Linear Transfer Function (LTF) Identification Method

173

(11)

Rules for Identifying Rational Distributed Lag Transfer Functions

184

(18)

Questions and Problems

193

(1)

Appendix 5A The Corner Table

194

(3)

Appendix 5B Transfer Function Identification Using Prewhitening and Cross Correlations

197

(5)

Building Dynamic Regression Models: Model Checking, Reformulation, and Evaluation

202

(51)

Diagnostic Checking and Model Reformulation

202

(7)

Evaluating Estimation Stage Results

209

(44)

Questions and Problems

215

(2)

Housing Starts and Sales

217

(15)

Industrial Production, Stock Prices, and Vendor Performance

232

(21)

Intervention Analysis

253

(37)

Introduction

253

(1)

Pulse Interventions

254

(5)

Step Interventions

259

(5)

Building Intervention Models

264

(8)

Multiple and Compound Interventions

272

(18)

Questions and Problems

276

(3)

Year-End Loading

279

(11)

Intervention and Outlier Detection and Treatment

290

(34)

The Rationale for Intervention and Outlier Detection

291

(1)

Models for Intervention and Outlier Detection

292

(7)

Likelihood Ratio Criteria

299

(14)

An Iterative Detection Procedure

313

(2)

Application

315

(4)

Detected Events Near the End of a Series

319

(5)

Questions and Problems

320

(1)

Appendix 8A BASIC Program to Detect AO, LS, and IO Events

321

(1)

Appendix 8B Specifying IO Events in the SCA System

322

(2)

Estimation and Forecasting

324

(18)

DR Model Estimation

324

(4)

Forecasting

328

(14)

Questions and Problems

340

(1)

Appendix 9A A BASIC Routine for Computing the Nonbiasing Factor in (9.2.24)

340

(2)

Dynamic Regression Models in a Vector ARMA Framework

342

(15)

Vector ARMA Processes

342

(3)

The Vector AR (π Weight) Form

345

(1)

DR Models in VAR From

346

(3)

Feedback Check

349

(5)

Check for Contemporaneous Relationship and Dead Time

354

(3)

Questions and Problems

356

(1)

Appendix

357

(5)

Table A Student's t Distribution

357

(2)

Table B χ2 Critical Points

359

(1)

Table C F Critical Points

360

(2)

Data Appendix

362

(14)

References

376

(5)

Index

381

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Forecasting With Dynamic Regression Models

Summary

Author Biography

Table of Contents

Supplemental Materials