A Spectral Domain Test for Stationarity of Spatio‐Temporal Data
A Spectral Domain Test for Stationarity of Spatio‐Temporal Data
复制标题
时空数据平稳性的谱域检验
DOI：
10.1111/jtsa.12222
复制
发表时间：
2017
影响因子：
0.9
通讯作者：
S. Subba Rao
中科院分区：
文献类型：
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作者：
S. Bandyopadhyay;C. Jentsch;S. Subba Rao
环境和地球物理科学中的许多随机现象都是空间和时间的函数;这些通常被称为时空过程。通常，时空过程是在离散的等距时间和空间中不规则间隔的位置上观察到的。一个重要的目标是根据观察结果建立统计模型。在这样做的时候，一个常用的假设是，潜在的时空过程是平稳的。如果这个假设不成立，那么均值或协方差函数都是错误的。例如，这可能导致不准确的预测。在这篇文章中，我们提出了一个时空平稳性的测试。该测试基于二分法，即如果过程是二阶平稳的，则随机过程的傅立叶变换几乎不相关，但如果过程是二阶非平稳的，则傅立叶变换相关。以此为动机，定义了离散等距时间上但不规则空间位置上的时空数据的离散傅立叶变换。提出了两种测量离散傅立叶变换相关度的统计量。这些统计量用于测试时空平稳性。结果表明，相同的统计量也可以适用于单向平稳性（空间或时间平稳性）的测试。所提出的方法进行了说明与一个小的模拟研究。
Many random phenomena in the environmental and geophysical sciences are functions of both space and time; these are usually called spatio‐temporal processes. Typically, the spatio‐temporal process is observed over discrete equidistant time and at irregularly spaced locations in space. One important aim is to develop statistical models based on what is observed. While doing so a commonly used assumption is that the underlying spatio‐temporal process is stationary. If this assumption does not hold, then either the mean or the covariance function is misspecified. This can, for example, lead to inaccurate predictions. In this article we propose a test for spatio‐temporal stationarity. The test is based on the dichotomy that Fourier transforms of stochastic processes are near uncorrelated if the process is second‐order stationary but correlated if the process is second‐order nonstationary. Using this as motivation, a discrete Fourier transform for spatio‐temporal data over discrete equidistant times but on irregularly spaced spatial locations is defined. Two statistics which measure the degree of correlation in the discrete Fourier transforms are proposed. These statistics are used to test for spatio‐temporal stationarity. It is shown that the same statistics can also be adapted to test for the one‐way stationarity (either spatial or temporal stationarity). The proposed methodology is illustrated with a small simulation study.