Multivariate Simultaneous Generalized ARCH

Engle, Robert F.; Kroner, Kenneth F.

doi:10.1017/s0266466600009063

Cited by 3,430 publications

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“…The right hand sides of the three equations above contain mainly quadratic terms and the matrix H t is indeed positive definite even "under very weak conditions," Engle and Kroner (1995). Moreover, the number of parameters to be estimated reduces to eleven, as compared to twenty one in the VECH model.…”

Section: Multivariate Garch Modelmentioning

confidence: 99%

International Stock Market Integration: Central and South Eastern Europe Compared

Horváth

Petrovski²

2012

SSRN Journal

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Section: Multivariate Garch Modelmentioning

confidence: 99%

International Stock Market Integration: Central and South Eastern Europe Compared

Horváth

Petrovski²

2012

SSRN Journal

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“…Engle and Kroner (1995) propose the following model for the conditional covariance matrix that generalizes to the multivariate case Bollerslev's (1986) univariate GARCH(1,1):…”

Section: Multivariate Garchmentioning

confidence: 99%

Small caps in international equity portfolios: the effects of variance risk

Guidolin¹,

Nicodano

2008

Ann Finance

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We show that predictable covariances between means and variances of stock returns may have a first order effect on portfolio composition. In an international asset menu that includes both European and North American small capitalization equity indices, we find that a three-state, heteroskedastic regime switching VAR model is required to provide a good fit to weekly return data and to accurately predict the dynamics in the joint density of returns. As a result of the non-linear dynamic features revealed by the data, small cap portfolios become riskier in bear markets, i.e. display negative co-skewness with other stock indices. Because of this property, a power utility investor ought to hold a well-diversified portfolio, despite the high risk premium and Sharpe ratios offered by small capitalization stocks. On the contrary small caps command large optimal weights when the investor ignores variance risk, by incorrectly assuming joint normality of returns. These results provide the missing partial equilibrium rationale for the presence of co-skewness in the empirical asset pricing models that have been proposed to explain the cross-section of stock returns.Keywords: intertemporal portfolio choice; return predictability; co-skewness and co-kurtosis; international portfolio diversification.JEL code: G11, G15, F30, C32. AbstractWe show that predictable covariances between means and variances of stock returns may have a first order effect on portfolio composition. In an international asset menu that includes both European and North American small capitalization equity indices, we find that a three-state,heteroskedastic Markov switching VAR model is required to provide a good fit to weekly return data and to accurately predict the dynamics in the joint density of returns. As a result of the non-linear dynamic features revealed by the data, small cap portfolios become riskier in bear markets, i.e. display negative co-skewness with other stock indices. Because of this property, a power utility investor ought to hold a well-diversified portfolio, despite the high risk premium and Sharpe ratios offered by small capitalization stocks. On the contrary small caps command large optimal weights when the investor ignores variance risk, by incorrectly assuming joint normality of returns. These results provide the missing partial equilibrium rationale for the presence of coskewness in the empirical asset pricing models that have been proposed to explain the cross-section of stock returns.2

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“…This is a modification of the Baba-Engle-Kraft-Kroner (BEKK) model (Engle and Kroner, 1995) in which the conditional covariance matrix H t does not regress on the residual process r t but depends on the activity of the signal. Hence, the model considered has only one innovation ε t and the variance (second order statistics) is coupled to the mean (first order statistics).…”

Section: The Model With Signal-dependent Noisementioning

confidence: 99%

“…A natural development was boosted by Engle's invention of the autoregressive conditional heteroskedasticity (ARCH) model (Engle, 1982) which was then extended to generalized ARCH (GARCH) models (Bollerslev, 1986) as well as multivariate case (Engle and Kroner, 1995). Along with the extension of the models is the growing interest in testing for causality in variance.…”

Section: Introductionmentioning

confidence: 99%

Granger causality with signal-dependent noise

2011

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It is generally believed that the noise variance in in vivo neuronal data exhibits time-varying volatility, particularly signal-dependent noise. Despite a widely used and powerful tool to detect causal influences in various data sources, Granger causality has not been well tailored for time-varying volatility models. In this technical note, a unified treatment of the causal influences in both mean and variance is naturally proposed on models with signal-dependent noise in both time and frequency domains. The approach is first systematically validated on toy models, and then applied to the physiological data collected from Parkinson patients, where a clear advantage over the classical Granger causality is demonstrated.© 2011 Elsevier Inc. All rights reserved. IntroductionThe past few years have witnessed a significant growth in the application of Granger causality to various research areas, especially to physiological recordings and functional MRI data. Proposed by Granger (1969) and further extended to the frequency domain by Geweke (1982), Granger causality has become a powerful tool to detect causal influences and functional connectivity from the huge amount of temporal data easily accessible nowadays.The classical Granger causal analysis is based on an autoregressive (AR) model (Friston, 2009a), which assumes that the current state of a process can be predicted by a linear function of its previous states plus a white noise or innovation process. A process is said to be the cause of another process if the inclusion of its past information can improve the prediction of the second process, i.e., reduce the variance of the prediction error. In spite of its easy implementation, wide justification and successful applications, some of the working assumptions might be an over-simplification when performing time series analysis in some situations. One particular scenario is the violation of time-invariant noise, that is, the volatility changes over time. As a common phenomenon in financial market series, similar characteristics have been observed in many physiological recordings, such as the data from epilepsy patients, Parkinson patients and so on. Because of the close relationship of many series, it is obvious to conjecture that changes in the volatility of one series may have an impact on the mean activity or volatility of another series and vice versa, which means that causal influences may happen on the second order statistics or there may be feedback between the first and second moments of the series. In these scenarios, a simple AR model obviously cannot capture these effects and a more detailed modeling of the volatility of the time series as well as the corresponding causality inference techniques are desired.The development of specific models for changing volatility, or say, conditionally heteroskedastic data, has long been launched, primarily motivated by the research in the literature of economics. A natural development was boosted by Engle's invention of the autoregressive conditional heteroskedasticity (...

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Multivariate Simultaneous Generalized ARCH

Cited by 3,430 publications

References 19 publications

International Stock Market Integration: Central and South Eastern Europe Compared

International Stock Market Integration: Central and South Eastern Europe Compared

Small caps in international equity portfolios: the effects of variance risk

Granger causality with signal-dependent noise

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