The Maximum of the Periodogram of a Sequence of Functional Data
研究了函数型数据序列的周期图算子，利用高斯近似理论推导了所有基频上最大范数的渐近分布，可用于检测周期未知的函数型时间序列中的周期信号。
We study the periodogram operator of a sequence of functional data. Using recent advances in Gaussian approximation theory, we derive the asymptotic distribution of the maximum norm over all fundamental frequencies. We consider the case where the noise variables are independent and then generalize our results to functional linear processes. Our theory can be used for detecting periodic signals in functional time series when the length of the period is unknown. We demonstrate the proposed methodology in a simulation study as well as on real data. Supplementary materials for this article are available online.