Functional Data Analysis And Its Applications In Financial Fields

In the modern society, accompanied with the progress of the data collectiontechniques, and the rapid spread of Internet technology and the extensive development,we can always easily access a large number of complex continuous data. How to dealwith these complex and continuous data poses a challenge to traditional statisticalmethods, especially in the financial sector, the trading time in trading day may lead totransactions the data generated as well as changes in how efficient continuous processof these high-frequency data is an important field of academic research. An importanttype of data is a unbalanced interval data of process. To solve these problems, theCanadian scholar Ramsay, first proposed a new data analysis ideas-Functional DataAnalysis (FDA). And compared to the traditional methods of statistical data analysis,functional data analysis which is a new non-parametric statistical analysis method canfully consider the issues to be analyzed from the point of dynamic stochastic processview. There are no parameter restrictions of traditional statistical methods, it is alsomore convenient to reflect and grasp the facts of inner behind. Functional dataanalysis treat the whole trajectory of the curve as a research unit, also it caneffectively solve the problem of data with unbalanced time intervals. In addition,functional data analysis can package the massive data. The basic idea of functionaldata analysis is treating function rather than discrete data as basic research units, toavoid information loss and distortion model estimation.Firstly, we summarized and reviewed the theoretical and applied research infunctional data analysis area, also we presented our basic research framework.Secondly we introduced the basic theory of the functional data analysis process,including functional principal component analysis, functional regression analysis andfunctional cluster analysis models. What’s more, we extend the functional principalcomponent analysis model, with traditional time series analysis methods, Intervalanalysis methods and so on. Finally, functional data analysis methods were applied tofinancial data analysis.The principal work of this paper is the extending the model of functionalcomponent analysis, also we conducted a preliminary exploration of the application offunctional data.