A1822
Title: Testing for sphericity of autocovariance matrix in high-dimensional time series
Authors: Mikoto Kita - Waseda University (Japan) [presenting]
Yousei Yoshida - Waseda University (Japan)
Yan Liu - Waseda University (Japan)
Abstract: The problem of testing the sphericity of autocovariance matrices for high-dimensional time series is studied. In the presence of temporal dependence, implementation of classical test statistics typically requires the estimation of long-run variances, which becomes increasingly challenging as the dimension grows. To address this issue, a bootstrap-based testing procedure is proposed that avoids explicit variance estimation. The method enforces the spherical structure under the null hypothesis at lag zero, while preserving the dependence structure at nonzero lags through tapered covariance estimation. This construction yields a feasible approach to inference in settings where direct variance estimation is difficult. The asymptotic validity of the proposed bootstrap is established for a class of test statistics under a general $(N, p)$-asymptotic framework, allowing for temporal dependence. In addition, explicit convergence rates are derived that reflect the joint effects of dimensionality and dependence. Simulation studies demonstrate that the proposed method achieves accurate size control and competitive power across a range of dependence structures.
