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Likelihood inference for a nonstationary fractional autoregressive model

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Author Info
Søren Johansen
Morten Ørregaard Nielsen () (School of Economics and Management, University of Aarhus, Denmark and CREATES)

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Abstract

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.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2007-33.

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Length: 45
Date of creation: 07 Nov 2007
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Handle: RePEc:aah:create:2007-33

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Related research
Keywords: Dickey-Fuller test; fractional unit root; likelihood inference;

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  2. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March. [Downloadable!] (restricted)
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  3. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-67, July. [Downloadable!] (restricted)
  4. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August. [Downloadable!]
  5. Nielsen, Morten rregaard, 2004. "Efficient Likelihood Inference In Nonstationary Univariate Models," Econometric Theory, Cambridge University Press, vol. 20(01), pages 116-146, February. [Downloadable!]
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  6. 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. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. 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. [Downloadable!]
  9. repec:cup:etheor:v:8:y:1992:i:2:p:241-57 is not listed on IDEAS
  10. Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March. [Downloadable!] (restricted)
  11. Ignacio N. Lobato & Carlos Velasco, 2005. "Efficient Wald Tests For Fractional Unit Roots," Economics Working Papers we056935, Universidad Carlos III, Departamento de Economía. [Downloadable!]
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  12. Johansen, S?ren, 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. [Downloadable!]
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  1. Morten Ørregaard Nielsen, 2008. "Nonparametric Cointegration Analysis of Fractional Systems With Unknown Integration Orders," Working Papers 1174, Queen's University, Department of Economics. [Downloadable!]
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