Testing for stationarity of functional time series in the frequency domain
Testing for stationarity of functional time series in the frequency domain
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DOI：
10.1214/19-aos1895
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发表时间：
2017-01
期刊：
影响因子：
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通讯作者：
Alexander Aue;A. Delft
中科院分区：
文献类型：
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作者：
Alexander Aue;A. Delft
最近，人们对函数时间序列的兴趣激增，涉及方法学和应用的论文发表速度大大加快。本文提出了一种新的基于频域方法的函数时间序列平稳性检验方法，为这方面的研究做出了贡献。所提出的检验统计量基于通过在所有傅立叶频率上的谱密度算子进行泛函主成分分析的联合降维，显式地允许依赖于频率的截断水平以适应潜在泛函时间序列的动态。分别在平稳函数时间序列的零假设和局部平稳函数时间序列的光滑替代下得到了检验的性质。通过渐近结果从理论上证明了该方法的合理性。来自模拟研究和对年温度曲线的应用的证据表明，该测试在有限样本中运行良好。
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.