Abstract
Whenever deterministic seasonality is ignored, the distribution of the Dickey-Fuller test is shifted to the left, with lower dispersion at the same time. When accounting for serial correlation, the distortions become less predictable. A Monte Carlo study confirms that the (augmented) Dickey-Fuller test without seasonal dummies is oversized and has little power at the same time, due to the need of lag augmentation. The effect of neglecting seasonal deterministics on the KPSS test for stationarity depends on the way the long-run variance is estimated.
Similar content being viewed by others
References
Andrews, D.W.K. (1991) Heteroskedasticity and Autocorrelation, Consistent Covariance Matrix Estimation. Econometrica 59, 817–858.
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., W.R. Bell, and R.B. Miller (1986) Unit Roots in Time Series Models: Tests and Implications. The American Statistician 40, 12–26.
Kwiatkowski, D., P.C.B. Phillips, P. Schmidt, and Y. Shin (1992) Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root. Journal of Econometrics 54, 159–178.
Lopes, A.S. (2002) Deterministic Seasonality in Dickey-Fuller Tests: Should we Care? CEMAPRE Working Paper 2002-1.
MacKinnon, J.G. (1991) Critical Values for Cointegration Testing. In: R.F. Engle and C.W.J. Granger (eds.) Long-Run Economic Relationships. Oxford: Oxford University Press, pp. 267–276.
Newey, W.K. and K.D. West (1987) A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix. Econometrica 55, 703–708.
Phillips, P.C.B. (1987) Time Series Regression with a Unit Root. Econometrica 55, 277–301.
Phillips, P.C.B., and S. Jin (2002) The KPSS Test with Seasonal Dummies. Economics Letters 77, 239–243.
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.
Taylor, A.M.R. (2003) Locally Optimal Tests against Unit Roots in Seasonal Time Series Processes. Journal of Time Series Analysis 24, 591–612.
Author information
Authors and Affiliations
Additional information
This is a shorter version of a working paper containing additional experimental evidence and the proofs of the propositions. The working paper is available online under http://www.wiwi.uni-frankfurt.de/~deme/ends_urt.pdf.
Rights and permissions
About this article
Cite this article
Demetrescu, M., Hassler, U. Effect of neglected deterministic seasonality on unit root tests. Statistical Papers 48, 385–402 (2007). https://doi.org/10.1007/s00362-006-0343-6
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s00362-006-0343-6