Abstract
This paper develops statistics for detecting the presence of a unit root in time series data against the alternative of stationarity. Unlike most existing procedures, the new tests allow for deterministic trend polynomials in the maintained hypothesis. They may be used to discriminate between unit root nonstationarity and processes which are stationary around a deterministic polynomial trend. The tests allow for both forms of nonstationarity under the null hypothesis. Moreover, the tests allow for a wide class of weakly dependent and possibly heterogenously distributed errors. We illustrate the use of the new tests by applying them to a number of models of macroeconomic behavior.
The first author gratefully acknowledges financial assistance from the College of Behavioral and Social Sciences at the University of Maryland. The paper has benefitted by the probing comments of two anonymous referees of an earlier version. The authors are also grateful to Peter Schmidt for helpful discussions.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Notes
Notable exceptions are the statistics developed in Perron (1987) which allow for structural breaks in the deterministic component of time series.
The univariate bounds test can also allow for structural breaks in the deterministic component of the maintained hypothesis. The interested reader is referred to Perron (1988) for applications of the bounds procedure which allow for structural breaks using φ(t, 9).
References
Bhargava, A.: 1986, ‘On the Theory of Testing for Unit Roots in Observed Time Series’, Review of Economic Studies, 53, 369–384.
Campbell, J. Y., and N. G. Mankiw: 1986, ‘Are Output Fluctuations Transitory?’, Working Paper No. 1916, National Bureau of Economic Research, May 1986.
Campbell, J. Y., and N. G. Mankiw: 1987, ‘Permanent and Transitory Components in Macroeconomic Fluctuations’, American Economic Review, Papers and Proceedings, 111-117.
Chan, K., J. C. Hung, and J. K. Ord: 1977, ‘A Note on Trend Removal Methods: The Case of Polynomial versus Variable Differencing’, Econometrica, 45, 737–744.
Cochrane, J. H.: 1986, ‘How Big is the Random Walk in GNP?’, mimeo, University of Chicago.
Corbae P. D., and S. Ouliaris: 1986, ‘Robust Tests for Unit Roots in the Foreign Exchange Market’, Economics Letters, 22, 375–80.
Corbae P. D., and S. Ouliaris: 1988, ‘Cointegration and Tests of Purchasing Power Parity’, Review of Economics and Statistics, 70, 508–511.
Corbae P. D., S. Ouliaris, and J. Zender: 1987, ‘Testing a Necessary Condition for Efficiency in the Forward Exchange Market’, University of Maryland Working Paper No. 25, College Park, Maryland, U.S.A.
Dickey D. A., and W. A. Fuller: 1979, ‘Distribution of the Estimators for Autoregressive Time Series with a Unit Root’, Journal of the American Statistical Association, 74, 427–431.
Dickey, D.A.: 1981, ‘Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root’, Econometrica, 49, 1057–1072.
Durlauf, S., and P. C. B. Phillips: 1987, ‘Trends versus Random Walks in Times Series Analysis’, Econometrica, forthcoming.
Engle, R. F., and C. W. J. Granger: 1987, ‘Co-Integration and Error Correction: Representation, Estimation and Testing’, Econometrica, 55, No. 2, 251–276.
Hall, P., and C. C. Heyde: 1980, Martingale Limit Theory and Its Applications, John Wiley, New York, New York, U.S.A.
Nelson, C. R., and H. Kang: 1982, ’spurious Periodicity in Inappropriately Detrended Time Series’, Econometrica, 49, 741–751.
Nelson, C. R., and C. I. Plosser: 1982, ‘Trends and Random Walks in Macroeconomic Times Series’, Journal of Monetary Economics, 10, 132–162.
Newey, W. K., and K. D. West: 1987, ‘A Simple, Positive Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix’, Econometrica, 55, 703–708.
Park, J. Y., and P. C. B. Phillips: 1988, ’statistical Inference in Regressions with Integrated Processes: Part I’, Econometric Theory, 4, 468–497.
Perron, P.: 1986, ‘Trend and Random Walks in Macroeconomic Time Scries: Further Evidence from a New Approach’, Department of Economics, University of Montreal, Montreal, Canada.
Perron, P.: 1987, ‘The Great Crash, the Oil Price Shock and the Unit Root Hypothesis’, Department of Economics, University of Montreal, Quebec, Canada.
Perron, P.: 1988, ‘The Humped-Shaped Behaviour of Macroeconomic Fluctuations’, Department of Economics, University of Montreal, Montreal, Canada.
Phillips, P. C. B.: 1987, ‘Time Series Regression with Unit Roots’, Econometrica, 55(2), 277–302.
Phillips, P. C. B.: 1988a, ‘Multiple Regression with Integrated Processes’, IMS/SIAM Conference Volume, forthcoming.
Phillips, P. C. B.: 1988b, ‘Weak Convergence to the Matrix Stochastic Integral \( \int\limits_0^1 {BdB'} \), Journal of Multivariate Analysis, 24, 252–264.
Phillips, P. C. B., and S. N. Durlauf: 1986, ‘Multiple Time Series with Integrated Variables’, Review of Economic Studies, 53, 473–496.
Phillips, P. C. B., and S. Ouliaris: 1987, ‘Asymptotic Properties of Residual Based Tests for Cointegration’, Cowlcs Foundation Discussion Paper No. 847.
Phillips, P. C. B., and S. Ouliaris: 1988 ‘Testing for Cointegration using Principal Components Methods’, Journal of Economic Dynamics and Control, 12, 205–230.
Phillips P. C. B., and P. Perron: 1988, ‘Testing for a Unit Root in Time Series Regression’, Biometrika, 75, 335–346.
Said, S. E., and D. A. Dickey: 1984, ‘Testing for Unit Roots in Autoregressive-Moving Average Models of Unknown Order’, Biometrika, 71, 599–607.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Ouliaris, S., Park, J.Y., Phillips, P.C.B. (1989). Testing for a Unit Root in the Presence of a Maintained Trend. In: Raj, B. (eds) Advances in Econometrics and Modelling. Advanced Studies in Theoretical and Applied Econometrics, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7819-6_2
Download citation
DOI: https://doi.org/10.1007/978-94-015-7819-6_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4048-0
Online ISBN: 978-94-015-7819-6
eBook Packages: Springer Book Archive