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CONVERGENCE TO STOCHASTIC POWER INTEGRALSFOR DEPENDENT HETEROGENEOUSPROCESSES

Published online by Cambridge University Press:  01 June 2009

Rickard Sandberg
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Abstract

Building on work of Hansen (1992, EconometricTheory 8, 489–501), we show weakconvergence for power transformations of integratedprocesses, with possibly serially correlated andheterogeneously distributed increments, tostochastic power integrals. The theory is applicablewhen testing the unit root or cointegrationhypothesis in nonlinear systems by regression-basedtest statistics.

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Type
Research Article
Information
Econometric Theory , Volume 25 , Issue 3 , June 2009 , pp. 739 - 747
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

This research has been supported by JanWallander’s Post Doctoral ScholarshipW2005-0103:1. The paper was written during my timeas a guest researcher at the Swedish Central bank,and I am thankful for a stimulating environment attheir research department. I thank two anonymousreferees for constructive and helpful suggestionsthat improved this paper. I also thank Tomas Björkand Annastiina Silvennoinen, who provided usefulremarks. The views expressed in this paper aresolely the responsibility of the author and shouldnot be interpreted as reflecting the views of theExecutive Board of Sveriges Riksbank.

References

REFERENCES

Billingsley, P. (1968) Convergence of Probability Measures. Wiley.Google Scholar
de Jong, R.M. & Wang, C.-H. (2005) Further results on the asymptotics for nonlinear transformations of integrated time series. Econometric Theory 21, 413–430.10.1017/S026646660505022XCrossRefGoogle Scholar
Granger, C.W.J. & Hallman, J. (1991) Nonlinear transformations of integrated time series. Journal of Time Series Analysis 12, 207–224.10.1111/j.1467-9892.1991.tb00078.xCrossRefGoogle Scholar
Granger, C.W.J. & Teräsvirta, T. (1993) Modelling Nonlinear Economic Relationships. Oxford University Press.CrossRefGoogle Scholar
Hansen, B.E. (1992) Convergence to stochastic integrals for dependent heterogeneous processes. Econometric Theory 8, 489–501.10.1017/S0266466600013189CrossRefGoogle Scholar
He, C. & Sandberg, R. (2006) Dickey-Fuller type of tests against non-linear dynamic models. Oxford Bulletin of Economics and Statistics 68, 835–861.10.1111/j.1468-0084.2006.00459.xCrossRefGoogle Scholar
Herrndorf, N. (1985) A functional central limit theorem for strongly mixing sequences of random variables. Probability Theory and Related Fields 69, 541–550.Google Scholar
Jansen, E.S. & Teräsvirta, T. (1996) Testing parameter constancy and super exogeneity in econometric equations. Oxford Bulletin of Economics and Statistics 58, 735–763.10.1111/j.1468-0084.1996.mp58004008.xCrossRefGoogle Scholar
Kapetanios, G., Shin, Y., & Snell, A. (2003) Testing for a unit root in the nonlinear STAR framework. Journal of Econometrics 112, 359–379.10.1016/S0304-4076(02)00202-6CrossRefGoogle Scholar
Kapetanios, G., Shin, Y., & Snell, A. (2006) Testing for cointegration in nonlinear smooth transition error correction models. Econometric Theory 22, 279–303.10.1017/S0266466606060129CrossRefGoogle Scholar
Kiliç, R. (2004) Linearity tests and stationarity. Econometrics Journal 7, 55–62.10.1111/j.1368-423X.2004.00121.xCrossRefGoogle Scholar
Kurtz, T.G. & Protter, P. (1991) Weak limit theorems for stochastic integrals and stochastic differential equations. Annals of Probability 19, 1035–1070.10.1214/aop/1176990334CrossRefGoogle Scholar
McLeish, D.L. (1975) A maximal inequality and dependent strong laws. Annals of Probability 3, 829–839.10.1214/aop/1176996269CrossRefGoogle Scholar
Newey, W.K. & West, K.D. (1987) A simple, positive definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 277–301.10.2307/1913610CrossRefGoogle Scholar
Park, J.Y. & Phillips, P.C.B. (1999) Asymptotics for nonlinear transformations of integrated time series. Econometric Theory 15, 269–298.10.1017/S0266466699153015CrossRefGoogle Scholar
Park, J.Y. & Phillips, P.C.B. (2001) Nonlinear regressions with integrated time series. Econometrica 69, 117–161.CrossRefGoogle Scholar
Phillips, P.C.B. (1987) Time series regression with a unit root. Econometrica 55, 277–301.10.2307/1913237CrossRefGoogle Scholar
Pötscher, B.M. (2004) Nonlinear functions and convergence to Brownian motion: Beyond the continuous mapping theorem. Econometric Theory 20, 1–22.10.1017/S0266466604201013CrossRefGoogle Scholar
Ramsey, J.B. (1969) Tests for specification errors in classical linear least squares regression analysis. Journal of the Royal Statistical Society, series B 31, 350–371.Google Scholar
Sims, C.A., Stock, J.H., & Watson, M.W. (1990) Inference in linear time series with some unit roots. Econometrica 58, 113–144.10.2307/2938337CrossRefGoogle Scholar