Functional Sieve Bootstrap for the Partial Sum Process With an Application to Change‐Point Detection
本文提出函数筛子自助法来估计弱平稳函数型时间序列部分和过程的分布，并用于基于CUSUM统计量的均值变点检验，证明了渐近有效性并通过模拟验证了有限样本表现。
ABSTRACT This article applies the functional sieve bootstrap (FSB) to estimate the distribution of the partial sum process for time series stemming from a weakly stationary functional process. Consistency of the FSB procedure under weak assumptions on the underlying functional process is established. This result allows for the application of the FSB procedure to testing for a change‐point in the mean of a functional time series using the CUSUM‐statistic. We show that the FSB asymptotically correctly estimates critical values of the CUSUM‐based test under the null‐hypothesis. Consistency of the FSB‐based test under local alternatives is also proven. The finite‐sample performance of the procedure is studied via simulations.