论文标题
多变量时间序列模型中的内核化Stein差异测试错误分布
Testing error distribution by kernelized Stein discrepancy in multivariate time series models
论文作者
论文摘要
知道错误分布在许多多元时间序列应用中很重要。为了减轻错误分布错误指定的风险，需要测试方法来检测所选错误分布是否正确。但是，大多数现有测试仅用于某些特殊的多元时间序列模型的多元正态分布，因此不能用于测试应用程序中经常观察到的重尾和偏斜的错误分布。在本文中，我们基于内核化的Stein差异为一般多元时间序列模型构建了新的一致测试。为了说明估计不确定性和未观察到的初始值，提供了一种bootstrap方法来计算临界值。对于大量的多元错误分布，我们的新测试易于实现，并且通过模拟和真实数据来说明其重要性。
Knowing the error distribution is important in many multivariate time series applications. To alleviate the risk of error distribution mis-specification, testing methodologies are needed to detect whether the chosen error distribution is correct. However, the majority of the existing tests only deal with the multivariate normal distribution for some special multivariate time series models, and they thus can not be used to testing for the often observed heavy-tailed and skewed error distributions in applications. In this paper, we construct a new consistent test for general multivariate time series models, based on the kernelized Stein discrepancy. To account for the estimation uncertainty and unobserved initial values, a bootstrap method is provided to calculate the critical values. Our new test is easy-to-implement for a large scope of multivariate error distributions, and its importance is illustrated by simulated and real data.
