Contemporaneous asymmetry in GARCH processes

Babsiri, Mohamed El; Zakoïan, Jean‐Michel

doi:10.1016/s0304-4076(00)00084-1

Cited by 47 publications

(34 citation statements)

References 45 publications

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“…Consider autoregressive volatility model (2), where λ t ≥ 0 are independent identically distributed non-negative random variables. To provide with conditions for the existence of a stationary volatility process we notice that it is equivalent to the following series being well defined…”

Section: Existence and Stationarity Conditionsmentioning

confidence: 99%

“…Let random variables λ i 's be as in (2). By m and σ 2 we denote their mean and variance, respectively.…”

Section: Moments Of ρ Tmentioning

confidence: 99%

“…It is well known to financial practitioners that the vast majority of data show various systematic asymmetries (see, for example [17] and [2]). Among them two have been subject of more thorough studies, namely asymmetry in the distribution of returns and asymmetry in the way volatility responds to positive and negative (relatively to the mean) returns.…”

Section: Introductionmentioning

confidence: 99%

“…However, it is interesting to note that the leverage can also increase from a decrease of the coefficient of variation for volatility. For example, the location parameter λ, presented in our extended model (2), enters through the coefficient of variation (cv 1 ) of volatility in (26). It is interesting to notice that the higher the value of λ, the stronger it will amplify the leverage effect in the data.…”

mentioning

confidence: 99%

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Tail Behavior and Dependence Structure in the APARCH Model

Javed

Podgórski

2016

Journal of Time Series Econometrics

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The APARCH model is a generalization of the GARCH model that attempts to capture asymmetric responses of returns and of volatility to positive and negative 'news shocks' -the phenomenon known as the leverage effect. Despite its potential, the model's mathematical properties have not yet been fully investigated. While the capacity of the model to account for the leverage effect is clear from its defining structure, little is known how the effect is quantified in terms of the model's parameters. The same applies to the quantification of heavy tails and time dependence. Here, in an attempt to fill this void, we study the model in further detail. We obtain sufficient conditions of its existence in different metrics as well as explicit forms of important characteristics: skewness, kurtosis, correlations and leverage. Utilizing these results, we analyze the roles of the parameters and discuss statistical inference. We also propose a natural extension by introducing an additional parameter and discuss how it affects the model. Through theoretical results and a Monte Carlo study we demonstrate that the model can produce heavy-tailed data. We illustrate these properties using S&P500 data as well as country indices for dominant European economies.

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Section: Existence and Stationarity Conditionsmentioning

confidence: 99%

“…Let random variables λ i 's be as in (2). By m and σ 2 we denote their mean and variance, respectively.…”

Section: Moments Of ρ Tmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Tail Behavior and Dependence Structure in the APARCH Model

Javed

Podgórski

2016

Journal of Time Series Econometrics

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“…3 While presenting this work at the 5th OxMetrics User Conference, Sébastien Laurent acquainted me with the article by El Babsiri and Zakoian (2001), whose basic idea of treating positive and negative returns asymmetrically is the same as the one we pursue in this paper. However, the model we propose is different from theirs and has the advantage of nesting other frequently used models such as the GARCH and the GJR-GARCH, both with possibly fat-tailed and skewed conditional distributions.…”

Section: The Modelmentioning

confidence: 99%

Modelling Good and Bad Volatility

Pelagatti

2009

Studies in Nonlinear Dynamics &Amp; Econometrics

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The returns of many financial assets show significant skewness, but in the literature this issue is only marginally dealt with. Our conjecture is that this distributional asymmetry may be due to two different dynamics in positive and negative returns. In this paper we propose a process that allows the simultaneous modelling of skewed conditional returns and different dynamics in their conditional second moments. The main stochastic properties of the model are analyzed and necessary and sufficient conditions for weak and strict stationarity are derived.An application to the daily returns on the principal index of the London Stock Exchange supports our model when compared to other frequently used GARCH-type models, which are nested into ours.

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2010

GARCH Models

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Contemporaneous asymmetry in GARCH processes

Cited by 47 publications

References 45 publications

Tail Behavior and Dependence Structure in the APARCH Model

Tail Behavior and Dependence Structure in the APARCH Model

Modelling Good and Bad Volatility

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