Estimation of Copula Models for Time Series of Possibly Different Lengths
Estimation of Copula Models for Time Series of Possibly Different Lengths
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DOI：
10.2139/ssrn.293423
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发表时间：
2001-11
期刊：
影响因子：
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通讯作者：
Andrew J. Patton
中科院分区：
文献类型：
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作者：
Andrew J. Patton
条件Copulas理论提供了一种构造灵活的多变量密度模型的方法，允许每个单独变量的条件密度随时间变化，以及变量之间的条件依赖关系随时间变化。此外，在构建这些模型时使用Copula通常允许将参数向量划分为仅与边际分布相关的元素和与Copula相关的元素。本文提出了一种两阶段(或多阶段)极大似然估计，用于这种划分是可能的情况。我们扩展了现有的关于Copula模型估计的统计学文献，以考虑表现出时间相关性和异质性的数据。估计器足够灵活，因此很容易处理每个变量上的数据量不相等的情况。我们在蒙特卡罗研究中研究了估计量的小样本性质，并发现它与标准的(一阶段)极大似然估计量相比表现得很好。最后，我们给出了该估计量在日日元-美元汇率和欧元-美元汇率联合分布模型中的应用。我们发现一些证据表明，捕捉非对称依赖的Copula比假设对称依赖的Copula表现得更好。
The theory of conditional copulas provides a means of constructing flexible multivariate density models, allowing for time varying conditional densities of each individual variable, and for time-varying conditional dependence between the variables. Further, the use of copulas in constructing these models often allows for the partitioning of the parameter vector into elements relating only to a marginal distribution, and elements relating to the copula. This paper presents a two-stage (or multi-stage) maximum likelihood estimator for the case that such a partition is possible. We extend the existing statistics literature on the estimation of copula models to consider data that exhibit temporal dependence and heterogeneity. The estimator is flexible enough that the case that unequal amounts of data are available on each variable is easily handled. We investigate the small sample properties of the estimator in a Monte Carlo study, and find that it performs well in comparisons with the standard (one-stage) maximum likelihood estimator. Finally, we present an application of the estimator to a model of the joint distribution of daily Japanese yen - U.S. dollar and euro - U.S. dollar exchange rates. We find some evidence that a copula that captures asymmetric dependence performs better than those that assume symmetric dependence.