Application Of Functional Data Analysis Method In GDP Research

With the rapid development of computer technology,people have collected more and more data,which makes the classical multivariate statistical analysis methods be limited.Therefore,functional data analysis methods have been proposed.Gross Domestic Product(GDP)is an important indicator to measure the economic status and development level of a country or region.This thesis mainly studies the theory of functional data analysis method and makes an empirical analysis of China's provincial GDP data.First of all,it introduces several methods of functional data preprocessing and makes empirical analysis on China's provincial annual GDP data and provincial quarterly data respectively.Research shows that B-spline basis has relatively good fitting effect for data with and without cyclic characteristics.In addition,the least square fitting method based on B-spline basis is improved for sparse functional data processing.Secondly,multivariate statistical principal component analysis method and functional principal component analysis method are discussed.The empirical analysis results of these two methods show that there are two main influencing factors for the fluctuation of GDP mean value in China's provinces,the pulling effect of large economic provinces is the main influencing factor.Finally,the systematic clustering analysis method and the functional clustering analysis method are discussed,and the cosine method of curve for calculating the distance between functional variables is proposed.The empirical analysis results of the two methods show that although the systematic clustering analysis method and the functional clustering analysis method process data from different angles,the results obtained have some similarities.The results show that the total GDP and development potential of each province in China can be divided into different categories by province.On the contrary,provinces with relatively backward economy have more room for development,and the state should increase its policy support to these provinces.