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On IGARCH and convergence of the QMLE for misspecified GARCH models

Author

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  • Anders Tolver Jensen

    (Department of Natural Sciences, University of Copenhagen)

  • Theis Lange

    (Department of Economics, University of Copenhagen & CREATES)

Abstract

We address the IGARCH puzzle by which we understand the fact that a GARCH(1,1) model fitted by quasi maximum likelihood estimation to virtually any financial dataset exhibit the property that alpha^hat + beta^hat is close to one. We prove that if data is generated by certain types of continuous time stochastic volatility models, but fitted to a GARCH(1,1) model one gets that alpha^hat + beta^hat tends to one in probability as the sampling frequency is increased. Hence, the paper suggests that the IGARCH effect could be caused by misspecification. The result establishes that the stochastic sequence of QMLEs do indeed behave as the deterministic parameters considered in the literature on filtering based on misspecified ARCH models, see e.g. Nelson (1992). An included study of simulations and empirical high frequency data is found to be in very good accordance with the mathematical results.

Suggested Citation

  • Anders Tolver Jensen & Theis Lange, 2009. "On IGARCH and convergence of the QMLE for misspecified GARCH models," CREATES Research Papers 2009-06, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2009-06
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    References listed on IDEAS

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    More about this item

    Keywords

    GARCH; Integrated GARCH; Misspecification; High frequency exchange rates;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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