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

Hill, Jonathan B.

doi:10.1007/978-1-4614-1653-1_10

Cited by 10 publications

(55 citation statements)

References 65 publications

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“…Nonparametric and semiparametric techniques are developed in Yatchew (1992), Hong and White (1995), Zheng (1996), Stute (1997), Koul and Stute (1999), Fan and Li (1996) and Stute and Zhu (2005) amongst many others. Hill (2012) delivers a robust asymptotic power one CM test for heavy tailed time series.…”

Section: An Interior Point Of ©mentioning

confidence: 99%

Stochastically weighted average conditional moment tests of functional form

Hill

2013

Studies in Nonlinear Dynamics and Econometrics

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We develop a new consistent conditional moment test of functional form based on nuisance parameter indexed sample moments first presented in Bierens (1982Bierens ( , 1990. We reduce the nuisance parameter space to known countable sets, which leads to a weighted average conditional moment test in the spirit of Bierens and Ploberger's (1997) Integrated Conditional Moment test. The weights are possibly stochastic in an arbitrary way, integer-indexed and flexible enough to cover a range of tests from average to higher quantile to maximum tests. The limit distribution under the null and local alternative belong to the same class as the ICM statistic, hence our test is admissible if the errors are Gaussian, and a flat weight leads to the greatest weighted average local power. * We thank two anonymous referees for their careful reading and feedback, and Editor Bruce Mizrach for helpful recommendations.

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Section: An Interior Point Of ©mentioning

confidence: 99%

Stochastically weighted average conditional moment tests of functional form

Hill

2013

Studies in Nonlinear Dynamics and Econometrics

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“…Francq and Zakoïan (2004, Theorem 3.2), however, show that the QML estimator requires y t itself to have a finite fourth moment, a tremendous requirement in practice since many finanncial time series show evidence of heavy tails (for evidence and further references, see Ibragimov, 2009;Aguilar and Hill, 2015;Hill, 2015b). theory relies heavily on uniform asymptotics for stationary mixing data, 2 hence whether our required results extend to non-stationary cases is not yet known.…”

Section: Introductionmentioning

confidence: 99%

“…The setting is motivated by recent intense interest in information theoretic methods (Smith, 1997;Imbens, 1997;Kitamura, 1997;Antoine, Bonnal, and Renault, 2007), including the higher order properties of GEL estimators (Newey and Smith, 2004;Anatolyev, 2005), coupled with empirical evidence that the distributions of many financial returns have very heavy tails (e.g. Embrechts, Kluppleberg, and Mikosch, 1997;Wagner and Marsh, 2005;Ibragimov, 2009;Hill, 2015b) and exhibit volatility clustering (Bollerslev, 1986).…”

Section: Introductionmentioning

confidence: 99%

“…However, over-identifying restrictions are not allowed, profiles weights are not developed and therefore efficient moment estimators are not treated, and the empirical likelihood method for inference is not considered. See also Hill (2013) for a related least squares theory for autoregressions. Notice, though, that moment conditions not used for estimation can always be tested using heavy tail robust methods (Hill and Aguilar, 2013), while a large variety of model specification tests can be rendered heavy tail robust (Hill, 2012;Hill and Aguilar, 2013;Aguilar and Hill, 2015).…”

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confidence: 99%

“…These moments are simple functions of trimming fractiles only in the case of iid errors, and otherwise we are limited to deducing bounds for these moments (see, e.g. Hill, 2012Hill, , 2015a which do not illuminate how trimming impacts higher order bias. Implicitly if q = 3 then x t (θ) = s t (θ), while q > 3 aligns with over-identifying restrictions E[( 2 t − 1)w i,t ] = 0 for i = 1, ..., q − 3.…”

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GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference

Hill

Prokhorov

2016

Journal of Econometrics

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We construct a Generalized Empirical Likelihood estimator for a GARCH(1,1) model with a possibly heavy tailed error. The estimator imbeds tail-trimmed estimating equations allowing for over-identifying conditions, asymptotic normality, efficiency and empirical likelihood based confidence regions for very heavy-tailed random volatility data. We show the implied probabilities from the tail-trimmed Continuously Updated Estimator elevate weight for usable large values, assign large but not maximum weight to extreme observations, and give the lowest weight to nonleverage points. We derive a higher order expansion for GEL with imbedded tailtrimming (GELITT), which reveals higher order bias and efficiency properties, available when the GARCH error has a finite second moment. Higher order asymptotics for GEL without tail-trimming requires the error to have moments of substantially higher order. We use first order asymptotics and higher order bias to justify the choice of the number of trimmed observations in any given sample. We also present robust versions of Generalized Empirical Likelihood Ratio, Wald, and Lagrange Multiplier tests, and an efficient and heavy tail robust moment estimator with an application to expected shortfall estimation. Finally, we present a broad simulation study for GEL and GELITT, and demonstrate profile weighted expected shortfall for the Russian Ruble -US Dollar exchange rate. We show that tail-trimmed CUE-GMM dominates other estimators in terms of bias, mse and approximate normality.Key words and phrases: GEL, GARCH, tail trimming, heavy tails, robust inference, efficient moment estimation, expected shortfall, Russian Ruble. AbstractWe construct a Generalized Empirical Likelihood estimator for a GARCH(1,1) model with a possibly heavy tailed error. The estimator imbeds tail-trimmed estimating equations allowing for over-identifying conditions, asymptotic normality, efficiency and empirical likelihood based confidence regions for very heavy-tailed random volatility data. We show the implied probabilities from the tail-trimmed Continuously Updated Estimator elevate weight for usable large values, assign large but not maximum weight to extreme observations, and give the lowest weight to non-leverage points. We derive a higher order expansion for GEL with imbedded tail-trimming (GELITT), which reveals higher order bias and efficiency properties, available when the GARCH error has a finite second moment. Higher order asymptotics for GEL without tail-trimming requires the error to have moments of substantially higher order. We use first order asymptotics and higher order bias to justify the choice of the number of trimmed observations in any given sample. We also present robust versions of Generalized Empirical Likelihood Ratio, Wald, and Lagrange Multiplier tests, and an efficient and heavy tail robust moment estimator with an application to expected shortfall estimation. Finally, we present a broad simulation study for GEL and GELITT, and demonstrate profile weighted expected shortfall for the ...

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Robust score and portmanteau tests of volatility spillover

Aguilar

Hill

2015

Journal of Econometrics

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

Cited by 10 publications

References 65 publications

Stochastically weighted average conditional moment tests of functional form

Stochastically weighted average conditional moment tests of functional form

GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference

Robust score and portmanteau tests of volatility spillover

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