Spatial Data Modeling Based On Copula Theory And Its Application In Temperature Data

Due to the abundant information,special structure and high complexity of spatial data,reasonable analysis of spatial data not only has important social and economic value,but also has important statistical significance.In the correlation analysis of spatial data,because copula function can describe the spatial correlation structure of spatial data,this method has been gradually used in spatial data modeling in recent years.Based on Copula theory,this paper uses c-vine and factor copula to model and analyze spatial data.Specifically,the work of this paper can be divided into the following two parts:(1)A spatial local c-vine composite likelihood analysis method is established for spatial data.Firstly,the density function of c-vine is introduced in the framework of compound likelihood,and the compound likelihood of local c-vine is obtained;Then,the spatial covariates are introduced to establish the regression model to estimate the parameters in binary copula,and the composite likelihood of spatial local c-vine is constructed;Finally,spatial information combined with c-vine structure can be used to interpolate and predict the data of unobserved position.Based on the temperature data and location information of 80 weather stations in Yunnan Province,three different regression models are established,and gets the spatial local C-Vine full model as the optimal model.The full model and the inverse distance weighting method are used to interpolate the temperature of the unknown point,and the interpolation effect of the full model is better when the unknown point is close to the adjacent weather station.(2)The analysis method of spatial factor copula model is established for spatial data.Specifically,the spatial factor model assumes that there is a common random factor in the study area that affects all spatial positions at the same time,and copula function can describe the spatial correlation structure of spatial data.The spatial factor copula model is obtained by combining copula theory with spatial factor model.Taking the temperature data and location information of 8 weather stations in Yunnan Province as the data set,the exponential spatial factor copula model and the traditional normal copula are used to interpolate the temperature of unknown points.The exponential spatial factor copula model can better capture the tail dependence.