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An Asymptotic Expansion in the Garch(1,1) Model

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Abstract

We develop order T^{-1} asymptotic expansions for the quasi-maximum likelihood estimator (QMLE) and a two step approximate QMLE in the GARCH(1,1) model. We calculate the approximate mean and skewness and hence the Edgeworth-B distribution function. We suggest several methods of bias reduction based on these approximation.

Suggested Citation

  • Oliver Linton, 1996. "An Asymptotic Expansion in the Garch(1,1) Model," Cowles Foundation Discussion Papers 1118, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1118
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    Cited by:

    1. Antonis Demos & Stelios Arvanitis, 2010. "Stochastic Expansions and Moment Approximations for Three Indirect Estimators," DEOS Working Papers 1004, Athens University of Economics and Business.
    2. Rodrigo Alfaro & Carmen Gloria Silva, 2008. "Measuring Equity Volatility: the case of Chilean Stock Index," Working Papers Central Bank of Chile 462, Central Bank of Chile.
    3. Antonis Demos & Stelios Arvanitis, 2010. "Stochastic Expansions and Moment Approximations for Three Indirect Estimators," DEOS Working Papers 1004, Athens University of Economics and Business.
    4. Emma M. Iglesias & Garry D. A. Phillips, 2012. "Estimation, Testing, and Finite Sample Properties of Quasi-Maximum Likelihood Estimators in GARCH-M Models," Econometric Reviews, Taylor & Francis Journals, vol. 31(5), pages 532-557, September.
    5. Dietmar P. J. Leisen, 2017. "The shape of small sample biases in pricing kernel estimations," Quantitative Finance, Taylor & Francis Journals, vol. 17(6), pages 943-958, June.
    6. Yong Bao, 2013. "On Sample Skewness and Kurtosis," Econometric Reviews, Taylor & Francis Journals, vol. 32(4), pages 415-448, December.

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