Whittle estimation in a heavy-tailed GARCH(1,1) model

Mikosch, Thomas; Straumann, Daniel

doi:10.1016/s0304-4149(02)00097-2

Cited by 42 publications

(24 citation statements)

References 19 publications

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“…That is why we think that the behavior of the process (X k ) k∈Z + is similar to GARCH models, where, even in the stable case, high moment conditions are needed for convergence of estimators such as the quasi-maximum likelihood estimator in Hall and Yao [5] or the Whittle estimator in Mikosch and Straumann [14].…”

Section: Resultsmentioning

confidence: 99%

Asymptotic behavior of CLS estimators for 2-type doubly symmetric critical Galton–Watson processes with immigration

Ispány¹,

Körmendi²,

Pap³

2014

Bernoulli

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Section: Resultsmentioning

confidence: 99%

Asymptotic behavior of CLS estimators for 2-type doubly symmetric critical Galton–Watson processes with immigration

Ispány¹,

Körmendi²,

Pap³

2014

Bernoulli

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“…Whittle [307] proposed an estimation technique that works in the spectral domain of the process (For further details about the Whittle estimation technique for ARMA processes see Brockwell and Davis [62].). Moreover, Mikosch and Straumann [228] showed that the Whittle estimator is consistent as long as the 4 th moment is finite and inconsistent when the 4 th moment is infinite. Thus, as noted by Mikosch and Straumann, the Whittle estimator for GARCH processes is unreliable as the ARCH models are applied in heavy-tailed data, sometimes without finite 5 th , 4 th , or even 3 rd moments.…”

Section: Other Estimating Methodsmentioning

confidence: 99%

Autoregressive Conditional Heteroscedasticity (ARCH) Models: A Review

Degiannakis

Xekalaki

2004

Quality Technology & Quantitative Management

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Autoregressive Conditional Heteroscedasticity (ARCH) models have successfully been employed in order to predict asset return volatility. Predicting volatility is of great importance in pricing financial derivatives, selecting portfolios, measuring and managing investment risk more accurately. In this paper, a number of univariate and multivariate ARCH models, their estimating methods and the characteristics of financial time series, which are captured by volatility models, are presented. The number of possible conditional volatility formulations is vast. Therefore, a systematic presentation of the models that have been considered in the ARCH literature can be useful in guiding one's choice of a model for exploiting future volatility, with applications in financial markets.

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“…Guo and Phillips (2001) consider IV estimation of (2) based on results from Kuersteiner (2002), where the instrument for Y 2 t 1 is an in…nite, weighted sum of W t 1 i for i 0. Giratis and Robinson (2001) and Mikosch and Straumann (2002) consider Whittle estimation for ARCH processes, which is asymptotically equivalent to constrained least squares and available in closed form when the spectral density of Y 2 t exists. Let E Y 2 t .…”

Section: Background and Motivationmentioning

confidence: 99%

Simple Estimators for ARCH Models

Prono

2016

FEDS

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Covariances between contemporaneous squared values and lagged levels form the basis for closed-form instrumental variables estimators of ARCH processes. These simple estimators rely on asymmetry for identi…cation (either in the model's rescaled errors or the conditional variance function) and apply to threshold ARCH(1) and ARCH(p) with p < 1 processes. Limit theory for these estimators is established in the case where the ARCH processes are regularly varying with a well-de…ned third and sixth moment of the raw returns and rescaled errors, respectively. The resulting limits are highly non-normal in empirically relevant cases, with slow rates of convergence relative to the thin-tailed p n-case. Nevertheless, Monte Carlo studies of a heavy-tailed ARCH(1) process show the simple IV estimator to outperform standard QMLE in (relatively) small samples when the data are (heavily) skewed. Methods for determining con…dence intervals for the ARCH estimates are also discussed.

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Whittle estimation in a heavy-tailed GARCH(1,1) model

Cited by 42 publications

References 19 publications

Asymptotic behavior of CLS estimators for 2-type doubly symmetric critical Galton–Watson processes with immigration

Asymptotic behavior of CLS estimators for 2-type doubly symmetric critical Galton–Watson processes with immigration

Autoregressive Conditional Heteroscedasticity (ARCH) Models: A Review

Simple Estimators for ARCH Models

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