Generalized Autoregressive Conditional Correlation

McAleer, Michael; Chan, Félix; Hoti, Suhejla; Lieberman, Offer

doi:10.1017/s0266466608080614

Cited by 147 publications

(155 citation statements)

References 23 publications

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“…Corollary 4 is consistent with the proof in McAleer et al (2008) that the QMLE of Full BEKK has no asymptotic properties, whereas the QMLE of Diagonal BEKK can be shown to be consistent and asymptotically normal.…”

Section: Corollarysupporting

confidence: 85%

“…In short, can be related directly to the data, , using equations (1) and (2). Ling and McAleer (2003) and McAleer et al (2008) provide general proofs of the asymptotic properties of univariate and multivariate conditional volatility models based on satisfying the regularity conditions in Jeantheau (1998) for consistency, and in Theorem 4.1.3 in Amemiya (1985) for asymptotic normality.…”

Section: Univariate Conditional Volatility Modelsmentioning

confidence: 99%

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The Fiction of Full BEKK: Pricing Fossil Fuels and Carbon Emissions

Chang

McAleer

2018

SSRN Journal

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The purpose of the paper is to (i) show that univariate GARCH is not a special case of multivariate GARCH, specifically the Full BEKK model, except under parametric restrictions on the off-diagonal elements of the random coefficient autoregressive coefficient matrix, that are not consistent with Full BEKK, and (ii) provide the regularity conditions that arise from the underlying random coefficient autoregressive process, for which the (quasi-) maximum likelihood estimates (QMLE) have valid asymptotic properties under the appropriate parametric restrictions. The paper provides a discussion of the stochastic processes that lead to the alternative specifications, regularity conditions, and asymptotic properties of the univariate and multivariate GARCH models. It is shown that the Full BEKK model, which in empirical practice is estimated almost exclusively compared with Diagonal BEKK (DBEKK), has no underlying stochastic process that leads to its specification, regularity conditions, or asymptotic properties, as compared with DBEKK. An empirical illustration shows the differences in the QMLE of the parameters of the conditional means and conditional variances for the univariate, DEBEKK and Full BEKK specifications KeywordsRandom coefficient stochastic process, Off-diagonal parametric restrictions, Diagonal BEKK, Full BEKK, Regularity conditions, Asymptotic properties, Conditional volatility, Univariate and multivariate models, Fossil fuels and carbon emissions. JEL Classification 1 AbstractThe purpose of the paper is to (i) show that univariate GARCH is not a special case of multivariate GARCH, specifically the Full BEKK model, except under parametric restrictions on the off-diagonal elements of the random coefficient autoregressive coefficient matrix, that are not consistent with Full BEKK, and (ii) provide the regularity conditions that arise from the underlying random coefficient autoregressive process, for which the (quasi-) maximum likelihood estimates (QMLE) have valid asymptotic properties under the appropriate parametric restrictions. The paper provides a discussion of the stochastic processes that lead to the alternative specifications, regularity conditions, and asymptotic properties of the univariate and multivariate GARCH models. It is shown that the Full BEKK model, which in empirical practice is estimated almost exclusively compared with Diagonal BEKK (DBEKK), has no underlying stochastic process that leads to its specification, regularity conditions, or asymptotic properties, as compared with DBEKK. An empirical illustration shows the differences in the QMLE of the parameters of the conditional means and conditional variances for the univariate, DEBEKK and Full BEKK specifications.

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Section: Corollarysupporting

confidence: 85%

Section: Univariate Conditional Volatility Modelsmentioning

confidence: 99%

The Fiction of Full BEKK: Pricing Fossil Fuels and Carbon Emissions

Chang

McAleer

2018

SSRN Journal

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“…For further details, see Ling and McAleer (2003) and McAleer et al (2008), who provide general proofs of the asymptotic properties of multivariate conditional volatility models based on satisfying the regularity conditions in Jeantheau (1998) for consistency, and in Theorem 4.1.3 in Amemiya (1985) for asymptotic normality.…”

Section: Advances In Economics Business and Management Research (Aebmentioning

confidence: 99%

A Simple Test for Causality in Volatility

Chang¹,

McAleer²

2017

Proceedings of the 2017 International Conference on Economics, Finance and Statistics (ICEFS 2017)

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Abstract. An early development in testing for causality (technically, Granger non-causality) in the conditional variance (or volatility) associated with financial returns, was the portmanteau statistic for non-causality in variance of Cheng and Ng (1996). A subsequent development was the Lagrange Multiplier (LM) test of non-causality in the conditional variance by Hafner and Herwartz (2006), who provided simulations results to show that their LM test was more powerful than the portmanteau statistic. While the LM test for causality proposed by Hafner and Herwartz (2006) is an interesting and useful development, it is nonetheless arbitrary. In particular, the specification on which the LM test is based does not rely on an underlying stochastic process, so that the alternative hypothesis is also arbitrary, which can affect the power of the test. The purpose of the paper is to derive a simple test for causality in volatility that provides regularity conditions arising from the underlying stochastic process, namely a random coefficient autoregressive process, and for which the (quasi-) maximum likelihood estimates have valid asymptotic properties under the null hypothesis of non-causality. The simple test is intuitively appealing as it is based on an underlying stochastic process, is sympathetic to Granger's (1969Granger's ( , 1988 notion of time series predictability, is easy to implement, and has a regularity condition that is not available in the LM test.

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“…In the case where A is a diagonal matrix, with a ii > 0 for all i = 1, ...., m, and | b ij |< 1| for all j = 1, ...., m, so that A has dimension m × m, McAleer et al [10] showed that the multivariate extension of GARCH(1,1) from equation (5) is given as the Diagonal BEKK model, namely:…”

Section: Introductionmentioning

confidence: 99%

“…It was shown in McALeer et al [10] that the QMLE of the parameters of the DBEKK model are consistent and asymptotically normal, so that standard statistical inference for testing hypotheses is valid. However, Chang and McAleer [4] demonstrate that this is not the case for the Full BEKK model.…”

Section: Introductionmentioning

confidence: 99%

Theoretical and Empirical Differences between Diagonal and Full BEKK for Risk Management

Allen

McAleer

2017

SSRN Journal

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The purpose of the paper is to explore the relative biases in the estimation of the Full BEKK model as compared with the Diagonal BEKK model, which is used as a theoretical and empirical benchmark. [4] show that univariate GARCH is not a special case of multivariate GARCH, specifically, the Full BEKK model, and demonstrate that Full BEKK which, in practice, is estimated almost exclusively, has no underlying stochastic process, regularity conditions, or asymptotic properties. Diagonal BEKK (DBEKK) does not suffer from these limitations, and hence provides a suitable benchmark. We use simulated financial returns series to contrast estimates of the The purpose of the paper is to explore the relative biases in the estimation of the Full BEKK model as compared with the Diagonal BEKK model, which is used as a theoretical and empirical benchmark. Chang and McAleer [4] show that univariate GARCH is not a special case of multivariate GARCH, specically, the Full BEKK model, and demonstrate that Full BEKK which, in practice, is estimated almost exclusively, has no underlying stochastic process, regularity conditions, or asymptotic properties. Diagonal BEKK (DBEKK) does not suffer from these limitations, and hence provides a suitable benchmark. We use simulated nancial returns series to contrast estimates of the conditional variances and covariances from DBEKK and BEKK. The results of non-parametric tests suggest evidence of considerable bias in the Full BEKK estimates. The results of quantile regression analysis show there is a systematic relationship between the two sets of estimates as we move across the quantiles. Estimates of conditional variances from Full BEKK, relative to those from DBEKK, are lower in the left tail and higher in the right tail. Chang and McAleer JEL Classification

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Generalized Autoregressive Conditional Correlation

Cited by 147 publications

References 23 publications

The Fiction of Full BEKK: Pricing Fossil Fuels and Carbon Emissions

The Fiction of Full BEKK: Pricing Fossil Fuels and Carbon Emissions

A Simple Test for Causality in Volatility

Theoretical and Empirical Differences between Diagonal and Full BEKK for Risk Management

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