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Closed-Form Estimation of Finite-Order ARCH Models: Asymptotic Theory and Finite-Sample Performance

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Abstract

Strong consistency and weak distributional convergence to highly non-Gaussian limits are established for closed-form, two stage least squares (TSLS) estimators for a class of ARCH(p) models. Conditions for these results include (relatively) mild moment existence criteria that are supported empirically by many (high frequency) financial returns. These conditions are not shared by competing closed-form estimators like OLS. Identification of these TSLS estimators depends on asymmetry, either in the model's rescaled errors or in the conditional variance function. Monte Carlo studies reveal TSLS estimation to sizably outperform quasi maximum likelihood estimation in (relatively) small samples. This outperformance is most pronounced when returns are heavily skewed.

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  • Todd Prono, 2016. "Closed-Form Estimation of Finite-Order ARCH Models: Asymptotic Theory and Finite-Sample Performance," Finance and Economics Discussion Series 2016-083, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgfe:2016-83
    DOI: 10.17016/FEDS.2016.083r1
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    Cited by:

    1. Todd Prono, 2017. "Regular Variation of Popular GARCH Processes Allowing for Distributional Asymmetry," Finance and Economics Discussion Series 2017-095, Board of Governors of the Federal Reserve System (U.S.).

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    More about this item

    Keywords

    ARCH; Closed form; Heavy tails; Instrumental variables; Regular variation; Two stage least squares;
    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
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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