Testing for a Unit Root with Near-Integrated Volatility
This paper considers tests for a unit root when the innovations follow a near-integrated GARCH process. We compare the asymptotic properties of the likelihood ratio statistic with that of the least-squares based Dickey-Fuller statistic. We first use asymptotics where the GARCH variance process is stationary with fixed parameters, and then consider parameter sequences such that the GARCH process converges to a diffusion process. In the fixed-parameter case, the asymptotic local power gain of the likelihood ratio test is only marginal for realistic parameter values. However, under near-integrated parameter sequences the difference in power is more pronounced.
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- Neil Shephard, 2005.
Economics Series Working Papers
2005-W17, University of Oxford, Department of Economics.
- H. Peter Boswijk & Jurgen A. Doornik, 1999.
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99-013/4, Tinbergen Institute.
- Jurgen A. Doornik & H. Peter Boswijk, 2005. "Distribution approximations for cointegration tests with stationary exogenous regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(6), pages 797-810.
- H. Peter Boswijk & Jurgen A. Doornik, 1999. "Distribution Approximations for Cointegration Tests with Stationary Exogenous Regressors," Tinbergen Institute Discussion Papers 99-013/4, Tinbergen Institute.
- Daniel B. Nelson & Dean P. Foster, 1994.
"Asypmtotic Filtering Theory for Univariate Arch Models,"
NBER Technical Working Papers
0129, National Bureau of Economic Research, Inc.
- Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January.
- Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
- repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
- repec:dgr:uvatin:2099013 is not listed on IDEAS
- Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
- Hansen, Bruce E., 1992. "Heteroskedastic cointegration," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 139-158.
- Hansen, Bruce E, 1995. "Regression with Nonstationary Volatility," Econometrica, Econometric Society, vol. 63(5), pages 1113-32, September.
- Lucas, André, 1997. "Cointegration Testing Using Pseudolikelihood Ratio Tests," Econometric Theory, Cambridge University Press, vol. 13(02), pages 149-169, April.
- Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
- Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038 Elsevier.
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