Testing serial independence of object-valued time series
提出一种完全非参数、无调节参数的方法，检验度量空间中对象值时间序列的序列独立性，能捕捉所有非线性成对依赖，并通过模拟和实际数据验证效果。
Summary 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 Cramér–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.