LASSO Estimation For Functional Principal Component Regression And Prediction Of Yield Rate

It is very important and meaningful to predict daily yield rate of stock market.In order to predict yield rate,many people usually use time series model such as ARIMA which is powerful in low-frequency data.With the development of financial market and information collecting,we can get more and more high-frequency data such as stock price per minute.Functional data analysis is a useful tool to deal with complicated data as it has fewer assumptions on data,which is more and more popular in financial market The main idea of functional data analysis is using nonparametric to change high-frequency data to functional data first,and then making an analysis on the curve.Functional linear regression deals with a scalar response by a regressor which is a random observed curve,its parameter is a curve.In order to estimate its functional coefficient,we can use Functional Principal Component Regression Estimator,Smooth Principal Component Regression Estimator,Penalized B-Splines Estimator,etcIn this paper,we mainly use Functional Principal Component Regression Estimator to estimate the parameter of functional linear regression and focus on the choice of eigenfunctions.As we know,in classical principal component analysis,we usually use scree plot and total contribution rate to choose principal components.In this paper,we use LASSO to choose eigenfunctions which are important to the functional coefficient.Different with other literatures,the data in this paper is repeated yield curves,which is dependent with each other.We show the convergence of sample covariance under weak dependence of samples.We compare classical method and LASSO method by simulation studies and an application of stock market.