Asymmetric multivariate normal mixture GARCH

Haas, Markus; Mittnik, Stefan; Paolella, Marc S.

doi:10.1016/j.csda.2007.12.018

Cited by 44 publications

(23 citation statements)

References 60 publications

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“…For example, Haas et al [47], Alexander and Lazar [48], Haas et al [49], Haas and Paolella [50] and Haas et al [51] use discrete normal mixture (MixN) GARCH models, with the MixN being a short-tailed distribution; Broda and Paolella [52] use a normal inverse Gaussian (NIG) structure, this having so-called semi-heavy tails (and existence of a moment generating function); several authors, including Mittnik and Paolella [53], Kuester et al [54], and Krause and Paolella [55] use an asymmetric Student's t distribution (this having heavy tails but such that the tail index lies in p0, 8q); Mittnik and Paolella [56] and Broda et al [57] use the asymmetric stable and mixtures of symmetric stable, respectively, these having heavy tails such that the tail index lies in p0, 2q. The fact that all of these methods can deliver highly accurate VaR forecasts confirms that the choice of asymptotic tail behavior and the (non-)existence of the second moment are not highly relevant for risk forecasting, but rather the use of a leptokurtic, asymmetric, bell-shaped distribution, in conjunction with a GARCH-type process.…”

Section: Critique Of the Stable Paretian Assumptionmentioning

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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Section: Critique Of the Stable Paretian Assumptionmentioning

confidence: 99%

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

Paolella

2016

Econometrics

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“…As in Haas, Mittnik, and Paolella (2009), we specify the latter as asymmetric BEKK processes, i.e. (cf.…”

Section: The Mixed Normal Bekk-garch (Mixn Bekk) Modelmentioning

confidence: 99%

“…For a broader perspective, we also include three multivariate GARCH models outside of the CCC or DCC families. Namely, we consider the BEKK model of Engle and Kroner (1995) which Gaussian and Student's t innovations, as well as the multivariate asymmetric mixed normal BEKK-GARCH (MixN BEKK) process of Haas, Mittnik, and Paolella (2009). As detailed in Appendix D, the latter specification combines a conditional mixture distribution with constant mixing weights with conditional regime-specific correlations which are time-varying according to a multivariate BEKK process.…”

Section: Application To Portfolio Selectionmentioning

confidence: 99%

“…The asymmetric normal mixture GARCH model in Haas, Mittnik, and Paolella (2009) is an asymmetric extension of the multivariate normal mixture GARCH process of Bauwens, Hafner, and Rombouts (2007). 20 With two mixture components, as in Section 4.3, the conditional distribution of the M-dimensional vector of shocks, , is a two-component normal mixture distribution with constant mixing weights p 1 ∈ (0, 1) and p 2 = 1 − p 1 , i.e.…”

Section: The Mixed Normal Bekk-garch (Mixn Bekk) Modelmentioning

confidence: 99%

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A multivariate regime-switching GARCH model with an application to global stock market and real estate equity returns

Haas

Liu

2018

Studies in Nonlinear Dynamics &Amp; Econometrics

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Abstract:We consider a multivariate Markov-switching GARCH model which allows for regime-specific volatility dynamics, leverage effects, and correlation structures. Conditions for stationarity and expressions for the moments of the process are derived. A Lagrange Multiplier test against misspecification of the within-regime correlation dynamics is proposed, and a simple recursion for multi-step-ahead conditional covariance matrices is deduced. We use this methodology to model the dynamics of the joint distribution of global stock market and real estate equity returns. The empirical analysis highlights the importance of the conditional distribution in Markovswitching time series models. Specifications with Student's t innovations dominate their Gaussian counterparts both in-and out-of-sample. The dominating specification appears to be a two-regime Student's t process with correlations which are higher in the turbulent (high-volatility) regime.

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“…A direct generalization of the MixNormal-GARCH model to the multivariate setting with D assets has been investigated by Bauwens et al (2007) and Haas et al (2009), the latter model allowing for asymmetries. While of value for a small number of assets, those models will not be practical for even modest portfolios, let alone large ones.…”

Section: Ica-mixstable-garchmentioning

confidence: 99%

Stable Mixture GARCH Models

et al. 2011

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A new model class for univariate asset returns is proposed which involves the use of mixtures of stable Paretian distributions, and readily lends itself to use in a multivariate context for portfolio selection. The model nests numerous ones currently in use, and is shown to outperform all its special cases. In particular, an extensive out-of-sample risk forecasting exercise for seven major FX and equity indices confirms the superiority of the general model compared to its special cases and other competitors. Estimation issues related to problems associated with mixture models are discussed, and a new, general, method is proposed to successfully circumvent these. The model is straightforwardly extended to the multivariate setting by using an independent component analysis framework. The tractability of the relevant characteristic function then facilitates portfolio optimization using expected shortfall as the downside risk measure. AbstractA new model class for univariate asset returns is proposed which involves the use of mixtures of stable Paretian distributions, and readily lends itself to use in a multivariate context for portfolio selection. The model nests numerous ones currently in use, and is shown to outperform all its special cases. In particular, an extensive out-of-sample risk forecasting exercise for seven major FX and equity indices confirms the superiority of the general model compared to its special cases and other competitors. Estimation issues related to problems associated with mixture models are discussed, and a new, general, method is proposed to successfully circumvent these. The model is straightforwardly extended to the multivariate setting by using an independent component analysis framework. The tractability of the relevant characteristic function then facilitates portfolio optimization using expected shortfall as the downside risk measure.

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Asymmetric multivariate normal mixture GARCH

Cited by 44 publications

References 60 publications

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

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

A multivariate regime-switching GARCH model with an application to global stock market and real estate equity returns

Stable Mixture GARCH Models

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