论文标题
希尔伯特空间估值时间序列的最大期刊图
The maximum of the periodogram of Hilbert space valued time series
论文作者
论文摘要
当周期的长度未知时，我们有兴趣检测希尔伯特空间值的周期信号。自然测试统计量是所有基本频率的期刊运算符的最大Hilbert-Schmidt标准。在本文中，我们分析了该测试统计量的渐近分布。我们考虑噪声变量是独立的情况，然后将结果推广到功能线性过程。实施测试的详细信息为功能自回归过程类别提供。我们通过检查奥地利格拉兹的空气质量数据来说明我们的方法的实用性。在模拟实验中评估了有限样品中渐近理论的准确性。
We are interested to detect periodic signals in Hilbert space valued time series when the length of the period is unknown. A natural test statistic is the maximum Hilbert-Schmidt norm of the periodogram operator over all fundamental frequencies. In this paper we analyze the asymptotic distribution of this test statistic. We consider the case where the noise variables are independent and then generalize our results to functional linear processes. Details for implementing the test are provided for the class of functional autoregressive processes. We illustrate the usefulness of our approach by examining air quality data from Graz, Austria. The accuracy of the asymptotic theory in finite samples is evaluated in a simulation experiment.
