Heavy-Tail and Plug-In Robust Consistent Conditional Moment Tests of Functional Form

Hill, Jonathan B.

doi:10.2139/ssrn.1914104

Cited by 5 publications

(2 citation statements)

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“…In general any value λ ∈ [0.02, 0.05] leads to roughly the same results. Similar trimming schemes are found to be highly successful in other robust estimation and inference contexts: see Hill [30,31] and Hill and Aguilar [33].…”

Section: Jb Hillmentioning

confidence: 83%

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Robust estimation and inference for heavy tailed GARCH

Hill

2015

Bernoulli

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We develop two new estimators for a general class of stationary GARCH models with possibly heavy tailed asymmetrically distributed errors, covering processes with symmetric and asymmetric feedback like GARCH, Asymmetric GARCH, VGARCH and Quadratic GARCH. The first estimator arises from negligibly trimming QML criterion equations according to error extremes. The second imbeds negligibly transformed errors into QML score equations for a Method of Moments estimator. In this case, we exploit a sub-class of redescending transforms that includes tail-trimming and functions popular in the robust estimation literature, and we re-center the transformed errors to minimize small sample bias. The negligible transforms allow both identification of the true parameter and asymptotic normality. We present a consistent estimator of the covariance matrix that permits classic inference without knowledge of the rate of convergence. A simulation study shows both of our estimators trump existing ones for sharpness and approximate normality including QML, Log-LAD, and two types of non-Gaussian QML (Laplace and Power-Law). Finally, we apply the tail-trimmed QML estimator to financial data.Comment: Published at http://dx.doi.org/10.3150/14-BEJ616 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

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Section: Jb Hillmentioning

confidence: 83%

“…See Hill and Aguilar [33] for references and simulation evidence. In terms of inference more choices exist, including test statistic functionals over λ like the supremum, and empirical process techniques for p-value computation (see Hill [30]).…”

Section: Jb Hillmentioning

confidence: 99%