Likelihood inference for a nonstationary fractional autoregressive model
This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. We consider the likelihood and its derivatives as stochastic processes in the parameters, and prove that they converge in distribution when the errors are i.i.d. with suitable moment conditions and the initial values are bounded. We use this to prove existence and consistency of the local likelihood estimator, and to .nd the asymptotic distribution of the estimators and the likelihood ratio test of the associated fractional unit root hypothesis, which contains the fractional Brownian motion of type II.
|Date of creation:||07 Nov 2007|
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- Lobato, Ignacio N. & Velasco, Carlos, 2005.
"Efficient wald tests for fractional unit roots,"
UC3M Working papers. Economics
we056935, Universidad Carlos III de Madrid. Departamento de Economía.
- Nielsen, Morten rregaard, 2004.
"Efficient Likelihood Inference In Nonstationary Univariate Models,"
Cambridge University Press, vol. 20(01), pages 116-146, February.
- Morten Oe. Nielsen, . "Efficient Likelihold Inference in Nonstationary Univariate Models," Economics Working Papers 2001-8, Department of Economics and Business Economics, Aarhus University.
- Juan J. Dolado & Jesus Gonzalo & Laura Mayoral, 2002. "A Fractional Dickey-Fuller Test for Unit Roots," Econometrica, Econometric Society, vol. 70(5), pages 1963-2006, September.
- 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.
- Andrews, Donald W.K., 1992.
"Generic Uniform Convergence,"
Cambridge University Press, vol. 8(02), pages 241-257, June.
- Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
- Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
- Peter C.B. Phillips, 1985.
"Time Series Regression with a Unit Root,"
Cowles Foundation Discussion Papers
740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
- Marinucci, D. & Robinson, P. M., 2000. "Weak convergence of multivariate fractional processes," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 103-120, March.
- Ling, Shiqing & Li, W.K., 2001. "Asymptotic Inference For Nonstationary Fractionally Integrated Autoregressive Moving-Average Models," Econometric Theory, Cambridge University Press, vol. 17(04), pages 738-764, August.
- P. M. Robinson & J. Hualde, 2003.
"Cointegration in Fractional Systems with Unknown Integration Orders,"
Econometric Society, vol. 71(6), pages 1727-1766, November.
- Peter M. Robinson & Javier Hualde, 2002. "Cointegration in Fractional Systems with Unknown Integration Orders," Faculty Working Papers 07/02, School of Economics and Business Administration, University of Navarra.
- Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August.
- Johansen, SØren, 2008. "A Representation Theory For A Class Of Vector Autoregressive Models For Fractional Processes," Econometric Theory, Cambridge University Press, vol. 24(03), pages 651-676, June.
- Newey, W.K., 1989.
"Uniform Convergence In Probability And Stochastic Equicontinuity,"
342, Princeton, Department of Economics - Econometric Research Program.
- Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-67, July.
- Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
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