Estimation of Partial Functional Linear Regression Model under Dependent Condition

Partial functional linear regression model refers to a type of regression machine that contains mixed functional and numerical data at the input and numerical data at the output. In the existing partial function linear regression machine estimation algorithm, it is assumed that functional data sample follow independent and identical distribution, which is inconsistent with the dependent characteristics of functional data in the financial and other fields. Therefore, the article first proposes two data-driven functional principal components representation methods for function data, then the regression coefficient function is regularized, and finally the estimation of the partial functional linear regression machine is transformed into the estimation of the multiple linear regression machine. The Monte Carlo simulation results show that the methods proposed in this paper have smaller parameter estimation errors and higher out-of-sample prediction accuracy when dealing with dependent data, the case analysis also shows the effectiveness in stock forecasting.