Book contents
- Frontmatter
- Contents
- Acknowledgments
- List of Contributors
- Introduction
- PART ONE CAUSALITY
- PART TWO INTEGRATION AND COINTEGRATION
- 5 Spurious Regression in Econometrics
- 6 Some Properties of Time Series Data and Their Use in Econometric Model Specification
- 7 Time Series Analysis of Error Correction Models
- 8 Co-Integration and Error-Correction: Representation, Estimation, and Testing
- 9 Developments in the Study of Cointegrated Economic Variables
- 10 Seasonal Integration and Cointegration
- 11 A Cointegration Analysis of Treasury Bill Yields
- 12 Estimation of Common Long Memory Components in Cointegrated Systems
- 13 Separation in Cointegrated Systems and Persistent-Transitory Decompositions
- 14 Nonlinear Transformations of Integrated Time Series
- 15 Long Memory Series with Attractors
- 16 Further Developments in the Study of Cointegrated Variables
- PART THREE LONG MEMORY
- Index
10 - Seasonal Integration and Cointegration
Published online by Cambridge University Press: 06 July 2010
- Frontmatter
- Contents
- Acknowledgments
- List of Contributors
- Introduction
- PART ONE CAUSALITY
- PART TWO INTEGRATION AND COINTEGRATION
- 5 Spurious Regression in Econometrics
- 6 Some Properties of Time Series Data and Their Use in Econometric Model Specification
- 7 Time Series Analysis of Error Correction Models
- 8 Co-Integration and Error-Correction: Representation, Estimation, and Testing
- 9 Developments in the Study of Cointegrated Economic Variables
- 10 Seasonal Integration and Cointegration
- 11 A Cointegration Analysis of Treasury Bill Yields
- 12 Estimation of Common Long Memory Components in Cointegrated Systems
- 13 Separation in Cointegrated Systems and Persistent-Transitory Decompositions
- 14 Nonlinear Transformations of Integrated Time Series
- 15 Long Memory Series with Attractors
- 16 Further Developments in the Study of Cointegrated Variables
- PART THREE LONG MEMORY
- Index
Summary
This paper develops tests for roots in linear time series which have a modulus of one but which correspond to seasonal frequencies. Critical values for the tests are generated by Monte Carlo methods or are shown to be available from Dickey–Fuller or Dickey–Hasza–Fuller critical values. Representations for multivariate processes with combinations of seasonal and zero-frequency unit roots are developed leading to a variety of autoregressive and error-correction representations. The techniques are used to examine cointegration at different frequencies between consumption and income in the U.K.
INTRODUCTION
The rapidly developing time-series analysis of models with unit roots has had a major impact on econometric practice and on our understanding of the response of economic systems to shocks. Univariate tests for unit roots were first proposed by Fuller (1976) and Dickey and Fuller (1979) and were applied to a range of macroeconomic data by Nelson and Plosser (1982). Granger (1981) proposed the concept of cointegration which recognized that even though several series all had unit roots, a linear combination could exist which would not. Engle and Granger (1987) present a theorem giving several representations of cointegrated series and tests and estimation procedures. The testing is a direct generalization of Dickey and Fuller to the hypothesized linear combination.
All of this work assumes that the root of interest not only has a modulus of one, but is precisely one.
- Type
- Chapter
- Information
- Essays in EconometricsCollected Papers of Clive W. J. Granger, pp. 189 - 211Publisher: Cambridge University PressPrint publication year: 2001