Testing error distribution by kernelized Stein discrepancy in multivariate time series models
Year: 2020
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Luo, Donghang, Zhu, Ke, Gong, Huan, Li, Dong
Institutions: University of Hong Kong, Tsinghua University
Language: English
Subfield: Signal Processing
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3046373267