BL-GARCH models and asymmetries in volatility

Storti, Giuseppe; Vitale, Cosimo Damiano

doi:10.1007/bf02511581

Cited by 23 publications

(14 citation statements)

References 15 publications

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“…Through this work, we have tried to study, in the first part the fundamental probabilistic properties of BL-GARCH (1, 2), basing on studies of Abdou Kâ Diongue, D. Guégan and R. C. Wolff [4] and G. Storti & Vitale [1], that have been made in this class of models. In the second part, we have studied the statistical inference, extended the model on panel data structure, and used one of efficient method well called composite likelihood that was introduced by Lindsay [6].…”

Section: Resultsmentioning

confidence: 99%

“…In front of these monetary and financial problems, Engle [2] proposed a new class of autoregressive conditionally heteroscedastic models (ARCH), followed by generalized ARCH or GARCH suggested by Bollerslev [3]. Storti and Vitale [1] proposed an innovative approach to modelling leverage effects in financial time series based on the Bilinear GARCH noted by BL-GARCH models which are considered as a generalization of GARCH models.…”

Section: Introductionmentioning

confidence: 99%

“…We focus on studies of Storti & Vitale [1] and Diongue & Guégan and Wolff [4], which they have well discussed and treated this class of models.…”

Section: Introductionmentioning

confidence: 99%

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Composite Likelihood for Bilinear GARCH Model

Bouchemella¹,

Benmostefa²

2014

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Composite Likelihood for Bilinear GARCH Model

Bouchemella¹,

Benmostefa²

2014

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“…The i-th component of the vector process y t under study follows a univariate BL-GARCH(1,1) process (Storti and Vitale 2003a) with conditional variance equation given by…”

Section: The Mbl-garch Modelmentioning

confidence: 99%

Modelling asymmetric volatility dynamics by multivariate BL-GARCH models

Storti

2007

Stat. Meth. & Appl.

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The class of Multivariate BiLinear GARCH (MBL-GARCH) models is proposed and its statistical properties are investigated. The model can be regarded as a generalization to a multivariate setting of the univariate BL-GARCH model proposed by Storti and Vitale (Stat Methods Appl 12:19–40, 2003a; Comput Stat 18:387–400, 2003b). It is shownhowMBL-GARCHmodels allowto account for asymmetric effects in both conditional variances and correlations. An EM algorithm for the maximum likelihood estimation of the model parameters is derived. Furthermore, in order to test for the appropriateness of the conditional variance and covariance specifications, a set of robust conditional moments test statistics are defined. Finally, the effectiveness of MBL-GARCH models in a risk management setting is assessed by means of an application to the estimation of the optimal hedge ratio in futures hedging

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“…These models are difficult to deal with because of their complex probabilistic structure (Tong, 1990). Therefore we focus on a particular bilinear model which is often used as a building block for much more complex non linear time series models such as the GARCH-BL (Storti, 2003).…”

Section: Introductionmentioning

confidence: 99%

The univariate distribution function for a particular bilinear model

Giordano

2004

Statistical Methods & Applications

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The aim of the paper is to find the univariate stationary distribution of a particular bilinear process. In this context, we propose a novel approach to derive the distribution function. It is based on a recursive formula and allows to relax the conditions on the moments of the process. We also show that the derived approximation converges to the "true" distribution function. The accuracy of the recursive formula is evaluated for finite sample dimensions by a small simulation study.

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BL-GARCH models and asymmetries in volatility

Cited by 23 publications

References 15 publications

Composite Likelihood for Bilinear GARCH Model

Composite Likelihood for Bilinear GARCH Model

Modelling asymmetric volatility dynamics by multivariate BL-GARCH models

The univariate distribution function for a particular bilinear model

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