A Statistical Test Approach For Moran's I On A Temporally Detrended Spatial-temporal Series

A spatio-temporal series is a set of multiple time series which are related to the space.It was thought that an analysis of spatio-temporal series is an expansion of time-series analysis in space.In order to make modelling,it is necessary to integrate spatial analysis method and time-series analysis method into an integrated spatio-temporal analytical one.In real word,spatio-temporal series often shows complex characteristics,such as long-range correlation in temporal dimension,spatio-temporal autocorrelation,and spatio-temporal heterogeneity.Spatio-temporal object is thus complicated.Since most of the geographical research simplifies specfied characteristics of the spatio-temporal object,the research results deviate from actual ones and bring a lot of difficulties in analyzing and mining the spatio-temporal data.Under this circumstance,theory and method for analyzing and modeling the spatio-temporal series thus is not developed very rapidly.Most of spatio-temporal analytical models are not capable of analyzing spatio-temporal autocorrelation directly because the assumption of spatio-temporal data in the presence of stationarity is voliated.Based on the previous studies,adequately regarding long-range correlation of a spatio-temporal series,a new temporally detrended spatio-temporal-series Moran's index(TDSTI)is given in this paper.We propose a statistical test method for TDSTI based on Monte Carlo(TDSTI statistical test),which is applied to analyze spatio-temporal autocorrelation of daily-temperature data from meteorological stations in Qinghai-Tibet Plateau vertical temperature zone,subtropical zone and warm temperate zone.The main research topics in this paper are as follows:(1)Propose a new spatio-temporal-series autocorrelation model based on long-range correlation series.Since spatio-temporal-series characteristics,such as nonstationarity and long-range correlation,violate the assumption of nonstationarity,which was supposed in previous spatio-temporal autocorrelation models.We thus proposed a new spatio-temporal autocorrelation model,applied for spatio-temporal autocorrelation analysis of nonstationary series:TDSTI model.(2)Propose a method of TDSTI statistical testMost of spatio-temporal series have complex cross-correlation because objects in their series are dependent.Classical statistical tests thereby can't be used to analyze theire cross-correlation.Based on Monte Carlo ideas and numerical simulation method,TDSTI statistical test method is presented in this study.Firstly,the ARFIMA(0,d,0)linear model was used to generate artificial simulation data,which has the same characteristics of long-range correlation and dynamic structure with the daily-temperature data from meteorological station in study area.Secondly,the spatio-temporal autocorrelation coefficients of TDSTI were calculated,and the significant statistical test results of TDSTI were given.Finally,the influencing degree of spatio-temporal series features and spatio-temporal weighting matrix features to TDSTI was analyzed.(3)Practical application and geographical analysesIn the end of this paper,daily temperature data from meteorological stations in Qinghai-Tibet Plateau vertical temperature zone,subtropical zone and warm temperate zone is utilized to analyze their spatio-temporal autocorrelation,and to presented their spatio-temporal autocorrelation statistical test.From perspectives of global and local spatio-temporal autocorrelation,we analyzed the traits of daily temperature spatio-temporal clustering and differentiation,and verified that TDSTI model is rationality and reliability.The analytical results indicated that:TDSTI model can measure the degree of spatio-temporal autocorrelation.Factors,such as length of the spatio-temporal series,time scale,strength of the spatio-temporal series,time lag and weight matrix structure,have comparativelystrong effects on the results of TDSTI model.However,factors,includingthe object permutation of spatio-temporal series and spatial range,have relatively weak impacts on the results.Although Monte Carlo approaches can detect statistical siginificance of spatio-temporal autocorrelation,its limitation is shown,which is applicable in specified reseach data.Different research data is needed to recompute critical values to determine their statistical significance.