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A Note on Asymptotic Power Calculations in Nearly Nonstationary Time Series

Published online by Cambridge University Press:  11 February 2009

Anders Rygh Swensen
Anders Rygh Swensen
Affiliation:
Central Bureau of Statistics of Norway
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Abstract

In the AR(2) model, with a double root at unity, we consider the asymptotic distribution of the likelihood ratio with respect to a nearly nonstationary alternative. It is shown how the distribution can be represented as a Radon-Nikodym derivative of an Ito process with respect to Brownian motion. Using this result, we point out how standard contiguity arguments can be applied to obtain a representation of the asymptotic power function in nearly nonstationary alternatives.

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Type
Articles
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Econometric Theory , Volume 9 , Issue 4 , August 1993 , pp. 659 - 667
Copyright
Copyright © Cambridge University Press 1993

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References

1.Chan, N.H.Inference for near-integrated time series with infinite variance. Journal of the American Statistical Association 85 (1990): 1069–1074.CrossRefGoogle Scholar
2.Chan, N.H. & Wei, C.Z.. Asymptotic inference for nearly nonstationary AR(1) processes. Annals of Statistics 15 (1987): 1050–1063.CrossRefGoogle Scholar
3.Chan, N.H. & Wei, C.Z.. Limiting distributions of least squares estimates of unstable autoregressive processes. Annals of Statistics 16 (1988): 367–401.CrossRefGoogle Scholar
4.Cox, D.D. & Llatas, I.. Maximum likelihood type estimation for nearly nonstationary autoregressive time series. Annals of Statistics 19 (1991): 1109–1128.CrossRefGoogle Scholar
5.Hájek, J. Local asymptotic minimax and admissibility in estimation. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability. Vol. I (1972): 175–194. Berkeley and Los Angeles: University of California Press, 1972.Google Scholar
6.Hájek, J. & Šidák, Z.. The Theory of Rank Tests. New York: Academic Press, 1967.Google Scholar
7.Jeganathan, P.On the asymptotic behavior of least-squares estimators in AR time series with roots near the unit circle. Econometric Theory 7 (1991): 269–306.CrossRefGoogle Scholar
8.Jeganathan, P.Some aspects of asymptotic theory with applications to time series models. Technical Report, University of Michigan: Ann Arbor (1988). Econometric Theory (forthcoming).Google Scholar
9.Johansen, S. The power function of the likelihood ratio test for cointegration. In Gruber, J. (ed.), Econometric Decision Models: New Methods of Modelling and Applications. New York: Springer-Verlag, 1990.Google Scholar
10.Kreiss, J-P.Local asymptotic normality for autoregression with infinite order. Journal of Statistical Planning and Inference 26 (1990): 185–219.CrossRefGoogle Scholar
11.Le Cam, L.Asymptotic Methods in Statistical Decision Theory. New York: Springer-Verlag, 1986.CrossRefGoogle Scholar
12.Lipster, R.S. & Shiryayev, A.N.. Statistics of Random Processes I, General Theory. New York: Springer-Verlag, 1977.Google Scholar
13.Phillips, P.C.B.Towards a unified asymptotic theory for autoregression. Biometrika 74 (1987): 535–547.CrossRefGoogle Scholar
14.Phillips, P.C.B.Regression theory for near-integrated time series. Econometrica 56 (1988): 1021–1043.CrossRefGoogle Scholar
15.Phillips, P.C.B.Partially identified econometric models. Econometric Theory 5 (1989): 181–240.CrossRefGoogle Scholar
16.Swensen, A.R.The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend. Journal of Multivariate Analysis 16 (1985): 54–70.CrossRefGoogle Scholar