The Econometric Analysis of Seasonal Time

Eric Ghysels and Denise R. Osborn provide a thorough and timely review of the recent developments in the econometric analysis of seasonal economic time series, summarizing a decade of theoretical advances in the area. The authors discuss the asymptotic distribution theory for linear nonstationary seasonal stochastic processes. They also cover the latest contributions to the theory and practice of seasonal adjustment, together with its implications for estimation and hypothesis testing. Moreover, a comprehensive analysis of periodic models is provided, including stationary and nonstationary cases. The book concludes with a discussion of some nonlinear seasonal and periodic models. The treatment is designed for an audience of researchers and advanced graduate students.

Foreword

xiii

Thomas J. Sargent

Preface

xv

List of Symbols and Notations

xix

Introduction to Seasonal Processes

1

(18)

Some Illustrative Seasonal Economic Time Series

1

(3)

Seasonality in the Mean

4

(8)

Deterministic Seasonality

4

(3)

Linear Stationary Seasonal Processes

7

(3)

Nonstationary Unit Root Processes

10

(2)

Unobserved Component Models

12

(1)

Periodic Processes

12

(3)

Seasonality in Higher Moments

15

(4)

Stochastic Seasonal Unit Roots

16

(1)

Seasonal GARCH

16

(1)

Periodic GARCH

17

(2)

Deterministic Seasonality

19

(23)

Introduction

19

(1)

Representations of Deterministic Seasonality

20

(4)

The Dummy Variable Representation

20

(1)

The Trigonometric Representation

21

(3)

Stochastic and Deterministic Seasonality

24

(6)

Stochastic Seasonal Processes

24

(2)

The Seasonal Random Walk

26

(2)

Deterministic Seasonality versus Seasonal Unit Roots

28

(1)

Unobserved Components Approaches

29

(1)

Testing Deterministic Seasonality

30

(12)

The Canova-Hansen Test

31

(5)

The Caner Test

36

(1)

The Tam-Reinsel Test

37

(2)

Some Comments

39

(3)

Seasonal Unit Root Processes

42

(51)

Introduction

42

(1)

Properties of Seasonal Unit Root Processes

43

(9)

The Seasonal Random Walk with Constant Drift

43

(2)

The Seasonal Random Walk with Seasonally Varying Drift

45

(1)

More General Stochastic Processes

45

(2)

Transformations and Seasonal Unit Roots

47

(3)

Asymptotic Distributions

50

(2)

Testing Seasonal Integration

52

(18)

Dickey-Hasza-Fuller Test

52

(2)

Testing a Unit Root of -- 1

54

(2)

Testing Complex Unit Roots

56

(4)

HEGY Test

60

(4)

The Kunst Test

64

(2)

The Osborn-Chui-Smith-Birchenhall Test

66

(2)

Multiple Tests and Levels of Significance

68

(2)

Extensions

70

(6)

Additional Dynamics

70

(1)

Deterministic Components

71

(1)

Structural Change in the Deterministic Components

72

(2)

Near Seasonal Integration

74

(1)

Higher Order Nonstationarity

75

(1)

Monte Carlo Studies

76

(4)

Comparisons of Test Procedures

77

(2)

Augmentation, Prewhitening, and Structural Breaks

79

(1)

Seasonal Cointegration between Variables

80

(10)

A Single Equation Approach

81

(3)

The Vector Approach

84

(4)

Seasonal Intercepts and Seasonal Cointegration

88

(2)

Some Remarks on Empirical Results

90

(3)

Seasonal Adjustment Programs

93

(28)

Introduction

93

(1)

Decompositions

93

(2)

The X-11 Program

95

(11)

The Linear X-11 Filter

95

(5)

On Potential Sources of Nonlinearity

100

(6)

The X-12 Seasonal Adjustment Program

106

(2)

RegARIMA Modeling in X-12-ARIMA

107

(1)

X-12 Diagnostics

108

(1)

The TRAMO/SEATS Programs

108

(7)

Unobserved Component ARIMA Models and Seasonal Adjustment

109

(3)

Model-Based Approach versus X-12

112

(3)

Seasonal Adjustment and Other Data Transformations

115

(6)

Estimation and Hypothesis Testing with Unfiltered and Filtered Data

121

(18)

Introduction

121

(1)

Linear Regression with Misspecified Seasonal Nonstationarity

122

(2)

The Classical Linear Regression Model and Filtering

124

(2)

Filtering of ARIMA Models

126

(5)

Filtering of Unit Root Processes

128

(1)

Filtering Stationary ARMA Processes

129

(2)

Finite Sample Approximations of Filtering Effects

131

(3)

Filtering and Cointegration

134

(2)

Bias Trade-Offs and Approximation Errors

136

(3)

Periodic Processes

139

(43)

Introduction

139

(1)

Some Simple Periodic Processes

140

(4)

Periodic Heteroskedasticity

141

(1)

Periodic MA(1) Process

142

(1)

Periodic AR(1) Process

143

(1)

Representations and Properties of Periodic Processes

144

(8)

The VAR Representation

144

(2)

Properties of Stationary PAR Processes

146

(2)

The Constant Parameter Representation of a PAR Process

148

(4)

Nonstationary Univariate PAR Processes

152

(16)

Types of Integration in a PAR Process

153

(2)

The Role of Intercept and Trend Terms

155

(2)

Testing for Seasonal Integration in a PAR Process

157

(3)

Cointegration Approaches to Testing Seasonal Integration

160

(4)

Testing Periodic and Nonperiodic Integration

164

(2)

Extensions: Augmentation and Deterministic Components

166

(2)

Periodic Cointegration

168

(12)

Some Issues in Periodic Cointegration

168

(3)

Vector Approaches to Periodic Cointegration

171

(3)

Nonperiodic, Periodic, and Seasonal Cointegration

174

(2)

The Boswijk-Franses Test for Periodic Cointegration

176

(3)

Generalizations

179

(1)

Some Comments on Empirical and Monte Carlo Analyses

180

(2)

Some Nonlinear Seasonal Models

182

(21)

Introduction

182

(1)

Stochastic Seasonal Unit Roots

183

(2)

Seasonal ARCH Models

185

(9)

The Class of Models

185

(3)

The Effects of Filtering on ARCH Models

188

(6)

Periodic GARCH Models

194

(4)

Periodic Markov Switching Models

198

(5)

Epilogue

203

(4)

Bibliography

207

(16)

Subject Index

223

(2)

Author Index

225

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The Econometric Analysis of Seasonal Time Series

Summary

Table of Contents

Supplemental Materials