Test of change point versus long‐range dependence in functional time series
提出一种显著性检验方法，用于区分函数型时间序列中带有变点的短记忆与长程依赖，基于投影系数和局部Whittle估计，并应用于日内资产价格曲线数据。
In the context of functional time series, we propose a significance test to distinguish between short memory with a change point and long range dependence. The test is based on coefficients of projections onto an optimal direction that captures the dependence structure of the latent stationary functions that are not observable due to a potential change point. The optimal direction must be estimated as well. The test statistic is constructed using the local Whittle estimator applied to these coefficients. It has standard normal distribution under the null hypothesis (change point) and diverges to infinity under the alternative (long range dependence). The article includes asymptotic theory, a simulation study and an application to curve‐valued time series derived from intraday asset prices.