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Book contents
- Frontmatter
- Contents
- Preface
- 1 Basic probability theory
- 2 Convergence
- 3 Introduction to conditioning
- 4 Nonliner parametric regression analysis and maximum likelihood theory
- 5 Tests for model misspecification
- 6 Conditioning and dependence
- 7 Functional specification of time series models
- 8 ARMAX models: estimation and testing
- 9 Unit roots and cointegration
- 10 The Nadaraya–Watson kernel regression function estimator
- References
- Index
9 - Unit roots and cointegration
Published online by Cambridge University Press: 28 October 2009
- Frontmatter
- Contents
- Preface
- 1 Basic probability theory
- 2 Convergence
- 3 Introduction to conditioning
- 4 Nonliner parametric regression analysis and maximum likelihood theory
- 5 Tests for model misspecification
- 6 Conditioning and dependence
- 7 Functional specification of time series models
- 8 ARMAX models: estimation and testing
- 9 Unit roots and cointegration
- 10 The Nadaraya–Watson kernel regression function estimator
- References
- Index
Summary
If a time series is modeled as an ARMA(p,q) process while the true datagenerating process is an ARIMA(p– 1,1,q) process, strange things may happen with the asymptotic distributions of parameter estimators. For example, if a time series process Yt is modeled as Yt = αYt−1 + Ut, with Ut Gaussian white noise and α assumed to be in the stable region (-1,1), while in reality the process is a random walk, i.e., ΔYt = Ut, then the OLS estimator αn of α (on the basis of a sample of size n) is n-consistent rather than √n-consistent, and the asymptotic distribution of n(αn-α) is non-normal. Therefore, in testing the hypothesis α = 1 standard asymptotic theory is no longer valid. See Fuller (1976), Dickey and Fuller (1979, 1981), Evans and Savin (1981, 1984), Said and Dickey (1984), Dickey, Hasza, and Fuller (1984), Phillips (1987), Phillips and Perron (1988), Hylleberg and Mizon (1989), and Haldrup and Hylleberg (1989), among others, for various unit root tests (all based on testing α = 1 in an AR model) and Schwert (1989) for a Monte Carlo analysis of the power of some of these tests. Moreover, see Diebold and Nerlove (1990) for a review of the unit root literature, and see Bierens (1993) and Bierens and Guo (1993) for alternative tests of the unit root hypothesis.
In this chapter we shall review and explain the most common unit root tests.
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- Chapter
- Information
- Topics in Advanced EconometricsEstimation, Testing, and Specification of Cross-Section and Time Series Models, pp. 179 - 211Publisher: Cambridge University PressPrint publication year: 1994