The Econometric Analysis of Seasonal Time Series

by Eric Ghysels , Denise R. Osborn

• ISBN13: 9780521562607
• ISBN10: 0521562600
• Format: Hardcover
• Copyright: 2001-06-18
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

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