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On the Univariate Representation of BEKK Models with Common Factors
Journal of Time Series Econometrics Pub Date : 2016-01-01 , DOI: 10.1515/jtse-2015-0002
Alain Hecq , Sébastien Laurent , Franz C. Palm

Abstract Simple low order multivariate GARCH models imply marginal processes with a lot of persistence in the form of high order lags. This is not what we find in many situations however, where parsimonious univariate GARCH(1,1) models for instance describe quite well the conditional volatility of some asset returns. In order to explain this paradox, we show that in the presence of common GARCH factors, parsimonious univariate representations can result from large multivariate models generating the conditional variances and conditional covariances/correlations. The diagonal model without any contagion effects in conditional volatilities gives rise to similar conclusions though. Consequently, after having extracted a block of assets representing some form of parsimony, remains the task of determining if we have a set of independent assets or instead a highly dependent system generated with a few factors. To investigate this issue, we first evaluate a reduced rank regressions approach for squared returns that we extend to cross-returns. Second we investigate a likelihood ratio approach, where under the null the matrix parameters have a reduced rank structure. It emerged that the latter approach has quite good properties enabling us to discriminate between a system with seemingly unrelated assets (e.g. a diagonal model) and a model with few common sources of volatility.

中文翻译:

具有共同因素的BEKK模型的单变量表示

摘要简单的低阶多元GARCH模型以高阶滞后的形式隐含着具有很多持久性的边际过程。但是,这并不是我们在许多情况下都能找到的,例如,简约的单变量GARCH(1,1)模型很好地描述了某些资产收益率的条件波动性。为了解释这种悖论,我们表明在存在通用GARCH因子的情况下,简约的单变量表示可以由大型的多变量模型生成,这些模型会产生条件方差和条件协方差/相关。但是,在条件波动率下没有任何传染效应的对角线模型得出了类似的结论。因此,在提取了代表某种形式简约性的资产块之后,确定我们是否拥有一组独立资产还是由几个因素生成的高度依赖系统仍然是任务。为了调查此问题,我们首先针对平方收益(递延至交叉收益)评估了降秩回归方法。其次,我们研究一种似然比方法,其中在零值下,矩阵参数具有降低的秩结构。结果表明,后一种方法具有很好的属性,使我们能够区分资产看似无关的系统(例如对角线模型)和很少具有常见波动性源的模型。在null下,矩阵参数的秩结构减少。结果表明,后一种方法具有很好的属性,使我们能够区分资产看似无关的系统(例如对角线模型)和波动率很少的模型。其中,在null下,矩阵参数具有降低的秩结构。结果表明,后一种方法具有很好的属性,使我们能够区分资产看似无关的系统(例如对角线模型)和波动率很少的模型。
更新日期:2016-01-01
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