Modelling Non-Stationary Economic Time Series

Co-integration, equilibrium and equilibrium correction are key concepts in modern applications of econometrics to real world problems. This book provides direction and guidance to the now vast literature facing students and graduate economists. Econometric theory is linked to practical issues such as how to identify equilibrium relationships, how to deal with structural breaks associated with regime changes and what to do when variables are of different orders of integration.

Simon P. Burke is a Lecturer in Economics at the University of Reading.

John Hunter is Lecturer in Economics at Brunel University.

Preface

vii

1 Introduction: Cointegration, Economic Equilibrium and the Long Run

1

(7)

2 Properties of Univariate Time Series

8

(30)

2.1 Introduction

8

(1)

2.2 Non-stationarity

8

(7)

2.3 Univariate statistical time series models and non-stationarity

15

(16)

2.4 Testing for non-stationarity in single series

31

(6)

2.5 Conclusion

37

(1)

3 Relationships Between Non-Stationary Time Series

38

(31)

3.1 Introduction

38

(1)

3.2 Equilibrium and equilibrium correction

38

(9)

3.3 Cointegration and equilibrium

47

(15)

3.4 Regression amongst cointegrated variables

62

(4)

3.5 Conclusion

66

(3)

4 Multivariate Time Series Approach to Cointegration

69

(59)

4.1 Introduction

69

(2)

4.2 The VMA, the VAR and VECM

71

(7)

4.3 The Smith-McMillan-Yoo form

78

(11)

4.4 Johansen's VAR representation of cointegration

89

(8)

4.5 Johansen's approach to testing for cointegration in systems

97

(8)

4.6 Tests of cointegration in VAR models

105

(13)

4.7 Alternative representations of cointegration

118

(8)

4.8 Conclusion

126

(2)

5 Exogeneity and Identification

128

(31)

5.1 An introduction to exogeneity

129

(8)

5.2 Identification

137

(14)

5.3 Exogeneity and identification

151

(3)

5.4 Empirical examples

154

(2)

5.5 Conclusion

156

(3)

6 Further Topics in the Analysis of Non-Stationary Time Series

159

(41)

6.1 Introduction

159

(1)

6.2 Inference and estimation when series are not I(1)

160

(13)

6.2 Forecasting in cointegrated systems

173

(15)

6.3 Models with short-run dynamics induced by expectations

188

(10)

6.4 Conclusion

198

(2)

7 Conclusions: Limitations, Developments and Alternatives

200

(3)

7.1 Approximation

200

(1)

7.2 Alternative models

201

(1)

7.3 Structural breaks

201

(1)

7.4 Last comments

202

(1)

Notes

203

(12)

Appendix A Matrix Preliminaries

215

(2)

A.1 Elementary Row Operations and Elementary Matrices

215

(1)

A.2 Unimodular Matrices

216

(1)

A.3 Roots of a Matrix Polynomial

216

(1)

Appendix B Matrix Algebra for Engle and Granger (1987) Representation

217

(2)

B.1 Determinant/Adjoint Representation of a Polynomial Matrix

217

(1)

B.2 Expansions of the Determinant and Adjoint about z E (0, 1]

217

(1)

B.3 Drawing out a Factor of z from a Reduced Rank Matrix Polynomial

218

(1)

Appendix C Johansen's Procedure as a Maximum Likelihood Procedure

219

(4)

Appendix D The Maximum Likelihood Procedure in Terms of Canonical Correlations

223

(2)

Appendix E Distribution Theory

225

(10)

E.1 Some Univariate Theory

225

(1)

E.2 Vector Processes and Cointegration

226

(1)

E.3 Testing the Null Hypothesis of Non-Cointegration

227

(1)

E.4 Testing a Null Hypothesis of Non-zero Rank

228

(3)

E.5 Distribution Theory when there are Deterministic Trends in the Data

231

(2)

E.6 Other Issues

233

(2)

Appendix F Estimation Under General Restrictions

235

(2)

Appendix G Proof of Identification based on an Indirect Solution

237

(2)

Appendix H Generic Identification of Long-run Parameters in Section 5.5

239

(1)

References

240

(10)

Index

250

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Modelling Non-Stationary Economic Time Series A Multivariate Approach

Summary

Author Biography

Table of Contents

Supplemental Materials