标题： 在频率域中测试函数时间序列的平稳性 显示英文标题

标题： Testing for stationarity of functional time series in the frequency domain

摘要： 近年来，人们对函数时间序列的兴趣激增，相关方法论和应用的论文发表速度大幅提高。 本文通过基于频域方法提出了一种新的函数时间序列平稳性检验，为该领域的研究做出了贡献。 所提出的检验统计量基于所有傅里叶频率下的谱密度算子的联合降维，即通过函数主成分分析实现，明确允许截断水平随傅里叶频率变化，以适应潜在函数时间序列的动力学特性。 在函数时间序列平稳性的零假设以及局部平稳函数时间序列的光滑替代假设下，推导了检验的性质。 通过渐近结果从理论上验证了该方法的有效性。 模拟研究和年平均温度曲线的实际应用结果表明，该检验在有限样本下表现良好。 显示英文摘要

摘要： Interest in functional time series has spiked in the recent past with papers covering both methodology and applications being published at a much increased pace. This article contributes to the research in this area by proposing a new stationarity test for functional time series based on frequency domain methods. The proposed test statistics is based on joint dimension reduction via functional principal components analysis across the spectral density operators at all Fourier frequencies, explicitly allowing for frequency-dependent levels of truncation to adapt to the dynamics of the underlying functional time series. The properties of the test are derived both under the null hypothesis of stationary functional time series and under the smooth alternative of locally stationary functional time series. The methodology is theoretically justified through asymptotic results. Evidence from simulation studies and an application to annual temperature curves suggests that the test works well in finite samples.