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摘要翻译：
多元GARCH时间序列模型的估计是一项困难的任务，主要是由于该问题所表现出的显着的过参数化，通常被称为“维数诅咒”。例如，在VEC族的情况下，模型中涉及的参数个数在问题的维数上以四阶多项式的形式增长。此外，这些参数还受到复杂的非线性约束，以确保模型设计中使用的条件协方差矩阵的平稳解的存在性和半正定性。到目前为止，这个问题在文献中只在具有强简约约束的低维情况下得到解决。本文给出了任意维估计问题的一般形式，并给出了求解该问题的Bregman-邻近信赖域方法。Bregman-prosulal方法允许我们在原始空间中以一种非常有效和自然的方式处理约束，信赖域机制稳定并加快了方案的速度。初步的计算实验证实了该方法的良好性能。
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英文标题：
《Multivariate GARCH estimation via a Bregman-proximal trust-region method》
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作者：
St\'ephane Chr\'etien and Juan-Pablo Ortega
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最新提交年份：
2011
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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英文摘要：
The estimation of multivariate GARCH time series models is a difficult task mainly due to the significant overparameterization exhibited by the problem and usually referred to as the "curse of dimensionality". For example, in the case of the VEC family, the number of parameters involved in the model grows as a polynomial of order four on the dimensionality of the problem. Moreover, these parameters are subjected to convoluted nonlinear constraints necessary to ensure, for instance, the existence of stationary solutions and the positive semidefinite character of the conditional covariance matrices used in the model design. So far, this problem has been addressed in the literature only in low dimensional cases with strong parsimony constraints. In this paper we propose a general formulation of the estimation problem in any dimension and develop a Bregman-proximal trust-region method for its solution. The Bregman-proximal approach allows us to handle the constraints in a very efficient and natural way by staying in the primal space and the Trust-Region mechanism stabilizes and speeds up the scheme. Preliminary computational experiments are presented and confirm the very good performances of the proposed approach.
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PDF链接：
https://arxiv.org/pdf/1101.5475
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