PM2.5 Data Analysis Based On Functional Data Analysis And Generalized Quantile Regression

Frequent occurrences of haze weather in Beijing make the concentration of PM2.5 and other air pollutants as a topic of social importance.So far,the historical data of PM2.5 concentration is building up.How to use the historical data of PM2.5 concentration to analyze the characteristics and patterns of data,and even make effective predictions on the future PM2.5 concentration,is of great significance.In this paper,we study the hourly data of PM2.5 concentration in Beijing.Our aims are exploring the characteristics and patterns of data,and trying to forecast the future hourly PM2.5 concentration.Functional principal component analysis is used to capture the overall level and daily volatility of PM2.5 data based on the perspective of functional data analysis.And in order to make effective predictions on the future PM2.5 concentration,we apply generalized quantile regression combining with functional data analysis.Seasonal adjustment is made for PM2.5 concentration data,and the random component is obtained;using generalized quantile regression characterizes the tail of the distribution;then obtaining the estimations of principal component functions and the principal component scores of generalized quantile function by functional principal component analysis and the truncated Karhuhen-Loeve expression;finally,a forecast of the future principal component scores using a vector autoregressive model including exogeneous variables directly yields a forecast of the generalized quantile curve.There are three advantages:(?)the principal component functions can capture the overall level and daily volatility of PM2.5 data by functional principal component analysis;(?)it does not require distributional assumptions for the tails curves and could describe the extreme case of pm2.5 data by characterized the tail of the distribution;(?)it is worth exploring to analyze and forecast the concentration data of PM2.5 in Beijing by the combination of generalized quantile regression and functional data analysis.Comparing DSC method and ARIMA model,we find our method in this paper could perform better than the other two models based on MAPE and MSPE.