Nonpararmetric Regression And Applications In Finance

Abstract

This thesis aims to study the methods of nonparametric regressions and a few applications in finance. In this thesis, we will introduce a review of basic knowledge of regression, particularly, nonparametric regression. Nonparametric regressions are methods of regression in which the forms of the regression function are nonlinear but, unlike nonlinear parametric regression, not specified by a model but rather determined from the data. The main methodologies presented in this thesis include Spline regression, Local regression, Kendall Theil regression, Quantile regression, Multivariate adaptive regression splines (MARS) and Conic multivariate adaptive regression splines(CMARS). Furthermore, we also study the numerical simulations in R programming for the nonparametric regression models and present applications.