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首页> 外文期刊>Journal of Time Series Analysis >A SPECTRAL DOMAIN TEST FOR STATIONARITY OF SPATIO-TEMPORAL DATA
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A SPECTRAL DOMAIN TEST FOR STATIONARITY OF SPATIO-TEMPORAL DATA

机译：时空数据平稳性的光谱域测试

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摘要

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.
机译：环境和地球物理科学中的许多随机现象是时空的函数。这些通常称为时空过程。通常，时空过程是在离散的等距时间内以及在空间中不规则间隔的位置观察到的。一个重要的目标是根据观察到的结果开发统计模型。这样做时，通常使用的假设是潜在的时空过程是平稳的。如果此假设不成立，则均值或协方差函数将被错误指定。例如，这可能导致不正确的预测。在本文中，我们提出了时空平稳性测试。该检验基于二分法，即如果过程是二阶平稳的，则随机过程的傅里叶变换几乎是不相关的，而如果过程是二阶非平稳的，则是相关的。以此为动机，定义了离散的傅立叶变换，用于离散的等距时间内但不规则间隔的空间位置上的时空数据。提出了两种测量离散傅立叶变换中相关度的统计量。这些统计数据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测试单向平稳性（空间平稳性或时间平稳性）。通过一个小型仿真研究说明了所提出的方法。

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