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Cholesky-GARCH models with applications to finance

机译：Cholesky-GARCH模型及其在金融中的应用

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摘要

Instantaneous dependence among several asset returns is the main reason for the computational and statistical complexities in working with full multivariate GARCH models. Using the Cholesky decomposition of the covari-ance matrix of such returns, we introduce a broad class of multivariate models where univariate GARCH models are used for variances of individual assets and parsimonious models for the time-varying unit lower triangular matrices. This approach, while reducing the number of parameters and severity of the positive-definiteness constraint, has several advantages compared to the traditional orthogonal and related GARCH models. Its major drawback is the potential need for an a priori ordering or grouping of the stocks in a portfolio, which through a case study we show can be taken advantage of so far as reducing the forecast error of the volatilities and the dimension of the parameter space are concerned. Moreover, the Cholesky decomposition, unlike its competitors, decompose the normal likelihood function as a product of univariate normal likelihoods with independent parameters, resulting in fast estimation algorithms. Gaussian maximum likelihood methods of estimation of the parameters are developed. The methodology is implemented for a real financial dataset with seven assets, and its forecasting power is compared with other existing models.
机译：在使用完整的多元GARCH模型时，多个资产收益之间的瞬时依赖性是造成计算和统计复杂性的主要原因。使用此类收益的协方差矩阵的Cholesky分解，我们引入了广泛的多元模型，其中单变量GARCH模型用于单个资产的方差，而简约模型用于时变单位下三角矩阵。与传统的正交和相关GARCH模型相比，该方法在减少参数数量和减少正定约束的严重性的同时，具有一些优点。它的主要缺点是可能需要对投资组合中的股票进行先验排序或分组，通过案例研究，我们证明可以利用这一点，从而减少了波动率的预测误差和参数空间的维数。关注。此外，Cholesky分解与其竞争对手不同，将正态似然函数分解为具有独立参数的单变量正态似然的乘积，从而得到了快速的估计算法。提出了参数估计的高斯最大似然方法。该方法是针对具有七个资产的真实金融数据集实施的，并将其预测能力与其他现有模型进行了比较。

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