Testing serial independence of object-valued time series

• 成果类型: Article
• 署名作者: Jiang, Feiyu; Gao, Hanjia; Shao, Xiaofeng
• 署名单位: Fudan University; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asad069
• 发表日期: 2024
• 页码: 925944
• 关键词: distance correlation; portmanteau test; spectral tests; dependence; covariance; hypothesis; bootstrap; dimension; models

摘要

We propose a novel method for testing serial independence of object-valued time series in metric spaces, which are more general than Euclidean or Hilbert spaces. The proposed method is fully nonparametric, free of tuning parameters and can capture all nonlinear pairwise dependence. The key concept used in this paper is the distance covariance in metric spaces, which is extended to the autodistance covariance for object-valued time series. Furthermore, we propose a generalized spectral density function to account for pairwise dependence at all lags and construct a Cramer-von Mises-type test statistic. New theoretical arguments are developed to establish the asymptotic behaviour of the test statistic. A wild bootstrap is also introduced to obtain the critical values of the nonpivotal limiting null distribution. Extensive numerical simulations and two real data applications on cumulative intraday returns and human mortality data are conducted to illustrate the effectiveness and versatility of our proposed test.