Testing Error Distribution by Kernelized Stein Discrepancy in Multivariate Time Series Models
针对多变量时间序列模型，提出一种基于核化斯坦因差异的误差分布检验方法，适用于厚尾、偏斜等非正态分布，并通过自助法处理估计不确定性。
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 existing tests only deal with the multivariate normal distribution for some special multivariate time series models, and thus cannot be used for testing the often observed heavy-tailed and skewed error distributions in applications. In this article, 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. As an extension, we also show how to test for the error distribution in copula time series models.