Estimation of stable distributions by indirect inference

García, René; Renault, Éric; Veredas, David

doi:10.1016/j.jeconom.2010.12.007

Cited by 60 publications

(57 citation statements)

References 49 publications

(61 reference statements)

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“…As an alternative to ML, we apply the indirect inference estimation method introduced by Gouriéroux et al (1993), which is a simulation-based technique suitable to solve difficult or intractable estimation problems. This method has already proved to be a valuable candidate for the estimation of the parameters of the stable distribution in Lombardi and Calzolari (2008) and Garcia et al (2011). The idea behind the IndInf estimation method is to replace the model of interest (true model) with an approximated model, which is easier to handle and estimate (auxiliary model).…”

Section: Estimation Methodsmentioning

confidence: 99%

“…In this paper we adapt their approach and integrate the GARCH and TGARCH models in the estimation procedure. As an alternative, we also apply the IndInf method, which proves to be a valuable alternative to estimate the stable parameters (Lombardi and Calzolari, 2008;Garcia et al, 2011). Section 4 gives a thorough description of the two estimation methods and of their practical implementation when estimating the parameters of symmetric stable (T)GARCH models as specified above.…”

Section: Symmetric α-Stable Garch-type Modelsmentioning

confidence: 99%

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Estimating GARCH-type models with symmetric stable innovations: Indirect inference versus maximum likelihood

Calzolari

Halbleib

Parrini

2014

Computational Statistics & Data Analysis

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Symmetric α-stable distribution GARCH-type models Indirect inference Maximum likelihood Leverage effects Student's t distribution a b s t r a c t Financial returns exhibit conditional heteroscedasticity, asymmetric responses of their volatility to negative and positive returns (leverage effects) and fat tails. The α-stable distribution is a natural candidate for capturing the tail-thickness of the conditional distribution of financial returns, while the GARCH-type models are very popular in depicting the conditional heteroscedasticity and leverage effects. However, practical implementation of α-stable distribution in finance applications has been limited by its estimation difficulties.The performance of the indirect inference approach using GARCH models with Student's t distributed errors as auxiliary models is compared to the maximum likelihood approach for estimating GARCH-type models with symmetric α-stable innovations. It is shown that the expected efficiency gains of the maximum likelihood approach come at high computational costs compared to the indirect inference method.

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Section: Estimation Methodsmentioning

confidence: 99%

Section: Symmetric α-Stable Garch-type Modelsmentioning

confidence: 99%

Estimating GARCH-type models with symmetric stable innovations: Indirect inference versus maximum likelihood

Calzolari

Halbleib

Parrini

2014

Computational Statistics & Data Analysis

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“…For example, the estimator of Kogon and Williams [83] is based on the sample characteristic function, is very fast to calculate, and results in estimates which are close in performance to the MLE (though less so for the asymmetry parameter); see Section 5.4 below. Another method is via indirect inference, which requires simulating stable realizations, but not evaluating its likelihood; see Lombardi and Veredas [84] and Garcia et al [85].…”

Section: Remarksmentioning

confidence: 99%

Stable-GARCH Models for Financial Returns: Fast Estimation and Tests for Stability

Paolella

2016

Econometrics

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A fast method for estimating the parameters of a stable-APARCH not requiring likelihood or iteration is proposed. Several powerful tests for the (asymmetric) stable Paretian distribution with tail index 1 ă α ă 2 are used for assessing the appropriateness of the stable assumption as the innovations process in stable-GARCH-type models for daily stock returns. Overall, there is strong evidence against the stable as the correct innovations assumption for all stocks and time periods, though for many stocks and windows of data, the stable hypothesis is not rejected.

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“…Since random numbers from α-stable distributions can be obtained straightforwardly, simulation-based methods such as IndInf and EMM are appealing, as it has been shown by Garcia, Renault and Veredas (2008) and Lombardi and Calzolari (2008). They both use a skewed-t distribution as auxiliary model.…”

Section: Examplementioning

confidence: 99%

The method of simulated quantiles

Dominicy

Veredas

2013

Journal of Econometrics

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We introduce an inference method based on quantiles matching, which is useful for situations where the density function does not have a closed form -but it is simple to simulateand/or moments do not exist. Functions of theoretical quantiles, which depend on the parameters of the assumed probability law, are matched with sample quantiles, which depend on observations. Since the theoretical quantiles may not be available analytically, the optimization is based on simulations. We illustrate the method with the estimation of α-stable distributions. A thorough Monte Carlo study and an illustration to 22 financial indexes show the usefulness of the method.Keywords: Quantiles, simulated methods, α-stable distribution, fat tails. We are grateful to Marcelo Fernandes, Marc Hallin and Marc Paolella, as well as the participants at the conferences in "recent developments in time series" (Rennes, France) and in "statistical inference in multivariate models and time-series models" (Kagoshima, Japan), the ECORE-KUL seminar, and the doctoral course on "fat-tailed distributions" in the University of Zurich for insightful remarks.

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Estimation of stable distributions by indirect inference

Cited by 60 publications

References 49 publications

Estimating GARCH-type models with symmetric stable innovations: Indirect inference versus maximum likelihood

Estimating GARCH-type models with symmetric stable innovations: Indirect inference versus maximum likelihood

Stable-GARCH Models for Financial Returns: Fast Estimation and Tests for Stability

The method of simulated quantiles

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