Testing the existence of moments and estimating the tail index of augmented garch processes

Christian Francq and Jean-Michel Zakoian

MPRA Paper from University Library of Munich, Germany

Abstract: We investigate the problem of testing finiteness of moments for a class of semi-parametric augmented GARCH models encompassing most commonly used specifications. The existence of positive-power moments of the strictly stationary solution is characterized through the Moment Generating Function (MGF) of the model, defined as the MGF of the logarithm of the random autoregressive coefficient in the volatility dynamics. We establish the asymptotic distribution of the empirical MGF, from which tests of moments are deduced. Alternative tests relying on the estimation of the Maximal Moment Exponent (MME) are studied. Power comparisons based on local alternatives and the Bahadur approach are proposed. We provide an illustration on real financial data, showing that semi-parametric estimation of the MME offers an interesting alternative to Hill's nonparametric estimator of the tail index.

Keywords: APARCH model; Bahadur slopes; Hill's estimator; Local asymptotic power; Maximal moment exponent; Moment generating function (search for similar items in EconPapers)
JEL-codes: C12 C58 (search for similar items in EconPapers)
Date: 2021
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:110511

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