Partial Functional Spatial Autocorrelation Model And Its Application

With the advent of the big data of era,all kinds of high-dimensional complex data can be seen everywhere.Facing the processing of this data,some scholars have proposed functional data analysis methods.Functional data is continuity and high dimension.In the analysis,such observation data should be regarded as a whole.At this time,the classical method is no longer applicable.The common analysis methods in functional data analysis are data variability analysis and linear regression analysis.The functional linear regression model is the correlation analysis between two kinds of data and above.However,the data observed in many fields not only the function data characteristics,but also spatial attributes.This paper proposes a new partial functional spatial regression model for the spatial data and functional data problems,and applies to the research of meteorological data.Firstly,this paper constructs a partial functional spatial autocorrelation(PFSAC)model with spatial correlation between response variables and random error terms,and covariates have both scalar data and functional data.Then,in the process of parameter estimation,the functional part of PFSAC model is truncated by the method of functional principal component basis function,then the maximum likelihood estimation method is used to estimate the parameters of the expanded model,and the asymptotic property of the parameters is proved.Considering the applicability of the model,this paper also adds the content of checking whether the response variables and error terms have spatial correlation and linear terms are significant.The simulation results shows the slope function and its estimation in the form of image,which shows that the model proposed in this paper is effective.In this paper,the air quality data,meteorological data and economic data of Fenwei plain in 2019 are analyzed by FPCA method,FSAR model and PFSAC model.The SO2 concentration curve is analyzed by functional principal component method,and the variation characteristics of SO2 concentration are discussed.The results show that the cumulative contribution rate of the first four principal components has reached more than 94%,combined with the actual situation,the variation characteristics of SO2 concentration are explained.The effect of hourly temperature on monthly mean SO2 was analyzed by FSAR model,and compared with the results of functional linear model,it was found that FSAR model had better fitting effect on SO2 concentration and temperature dataThe effect of hourly temperature on monthly mean SO2 was analyzed by functional spatial autoregressive model,and compared with the results of functional linear model,it was found that FSAR model had better fitting effect on SO2 concentration and temperature data.The partial functional spatial regression model proposed in this paper is used to analyze the impact of regional GDP and hourly temperature curve on SO2 effect of concentration.Compared with the analysis results of generalized spatial regression model,it is found that partial functional spatial regression model is indeed better than generalized spatial regression model.At the same time,the dynamic analysis of temperature curve shows that the monthly rise of temperature has little influence on SO2 concentration,it has a great influence on the concentration of SO2 when it decreases.