CONTENTS

Xlll

12.5 DFFITS and Bounded Influence Estimation 487

12.6 Model Selection 490

12.7 Selection of Regressors 496

12.8 Implied F-Ratios for the Various Criteria 500

12.9 Cross-validation 504

12.10 Hausmans Specification Error Test 506

12.11 The Plosser-Schwert-White Differencing Test 513

12.12 Tests for Nonnested Hypotheses 514 Summary 518

Exercises 521

Appendix to Chapter 12 523

Introduction to Time-Series Analysis 525

13.1 Introduction 525

13.2 Two Methods of Time-Series Analysis: Frequency Domain and Time Domain 526

13.3 Stationary and Nonstationary Time Series 527

13.4 Some Useful Models for Time Series 530

13.5 Estimation of AR, MA, and ARMA Models 537

13.6 The Box-Jenkins Approach 542

13.7 /?easures in Time-Series Models 549 Summary 553

Exercises 553 Data Sets 555

Vector Autoregressions, Unit Roots,

and Cointegration 577

14.1 Introduction 578

14.2 Vector Autoregressions 578

14.3 Problems with VAR Models in Practice 580

14.4 Unit Roots 581

14.5 Unit Root Tests 582

14.6 Cointegration 588

14.7 The Cointegrating Regression 590

14.8 Vector Autoregressions and Cointegration 592

14.9 Cointegration and Error Correction Models 597

14.10 Tests for Cointegration 598

14.11 Cointegration and Testing of the REH and MEH 599

14.12 A Summary Assessment of Cointegration 601 Summary 602

Exercises 603

APPENDIX: Tables 609

Author Index 623

Subject Index 627

Preface

There have been many important developments in econometrics during the last two decades, but introductory books in the field still deal mostly with what econometrics was in the 1960s. The present book is meant to familiarize students (and researchers) with some of these developments, explaining them with very simple models without cluttering up the exposition with too much algebraic detail. Where proofs involve complicated expressions they are omitted and appropriate references are given. Ten of the more difficult sections have been marked with an asterisk indicating that they are optional. Beginning students can skip them and proceed. The book also contains several examples illustrating the techniques at each stage, and where illustrations are not given, some data sets have been provided so that students can compute the required results themselves.

Since the book covers quite a few topics, only a few examples have been given to illustrate each point. Giving too many illustrations for a single point might be boring for some students and would have made the book much too bulky. The instructors manual contains more illustrative examples and questions and answers. The exercises given at the end of each chapter are somewhat challenging. However, the instructors manual contains answers or guidelines. The instructors manual also gives a "guided tour" of the material in each chapter as well as some detailed explanations for some points that are touched briefly in the book.

Some of the questions at the end of the chapters have been taken from the examinations at several U.S. and U.K. universities, and from P. C. B. Phillips and M. R. Wickens, Exercises in Econometrics (Cambridge, Massachusetts, Ballinger Publishing Co., 1978), Vol. I. (Many of the questions in that book are from examinations in the U.K. universities.) Since questions tend to get repeated with minor changes, I have not bothered to quote the exact source for each question.

There are many distinguishing features of the book, some of which are: