Existence Test Of Spatiotemporal Structuring Effects Based On Gridded Spatiotemporal Data

In recent years,spatio-temporal data has been widely used in the fields of society,economy,environment and so on.It is of great valuable to detect the existence of spa-tiotemporal structured effects before modeling the data.After a specific model is fitted,the model diagnosis can also be done by the test of structured effect existence for the residuals.Therefore,it is of great importance to provide a reliable approach for testing the existence of spatiotemporal structured effects.This paper is concerned with the existence test of the structured effect for the station?ary spatiotemporal stochastic process on lattice.The test statistic is constructed as follows.First,an autocorrelation estimator is built based on the spatial Moran's Index.The asymp-totic distribution of the estimator is investigated,with its independence among different lags,under the null that no structured effects exist.Then,the original test is transformedby introducing a spatial statistic.At each fixed time,a spatial statistic is introduced,by which,the test of the structured effect existence is transformed to be a goodness-of-fit test.Last,the proposed statistic and its modified version are constructed.By using the Kolmogorov-Smirnov statistic,the test statistic for detecting the existence of the structured effects is provided,with its modified version for small spatial observations as well.A simulation study shows that the proposed test can not only control the probabilityof committing type I error,but also perform well in view of the power.Case studies il?lustrate that there exist some structured effects for the data from the National Oceanic and Atmospheric Administration.Based on the spatial Moran~5s Index and the methods of white noise test in time se?ries,the proposed test does not depend on the specific space-time model,and avoids the operation of high-dimensional correlation matrix inversion.Then,the test of the structured effect existence is cleverly transformed to be a goodness-of-fit test.