Expectile Regression Neural Network Model With Applications

The nonlinear natures of financial system are important factors that cause many complex phenomena in the financial market.They have attracted more and more attentions from acdemics and practitioners.In practice,it is difficult to characterize the complex features of financial markets using traditional linear models.With the development of artifical intelligence,neural networks have been successfully introduced into financial econometrics and applied to construct models for exploring the true laws in financial market.Similar to quantile regression,expectile regression can also reveal the internal mechanism and operating rules in financial system for more details.Recently,nonlinear expectile regression becomes popular because it can not only explore nonlinear relationships among variables,but also describe the complete distribution of a response variable conditional on given values of covariates.However,the traditional nonlinear expectile regression mainly has two shortcomings.First,it is difficult to select an appropriate form of a nonlinear function.Second,it ignores the interaction effects among covariates.In this dissertation,we develop a new expectile regression neural network model(ERNN)through adding a neural network structure to expectile regression approach.In addition,we also provide techniques of model estimation and method selection.To the best of our knowledge,a model with complex structure often leads to over-fitting.Therefore,we consider the expectile regression neural network with penalty term,including L2 penalty,L1 penalty and L1+L2 penalty,and discuss their modeling techniques.The advantage of ERNN model is illustrated by Monte Carlo simulation studies.In Monte Carlo numerical simulation,the expectile regression neural network with penalty term is compared with the traditional nonlinear expectile regressions.The results show that:(1)the ERNN model outperforms the conventional expectile regression in terms of predictive ability both in-sample and out-of-sample test;(2)the neural network with penalty term improve the model's predictive abilities.Finally,we successfully apply the ERNN models to investigate the behavior of housing price in China and United States.The empirical results show that the expectile regression neural network with penalty term is better than the traditional nonlinear expectile regression.Further more,we design a marginal analysis to examine the marginal contribution of covariates to housing price and obtain promising emprical results.To sum up,the proposed an expectile regression neural network is an extention of the conventional expectile regression from the theoritical perspection.We further develop three versions of ERNN models by using regularization methods such as L2 penalty,L1 penalty and L1+L2 penalty.In practical,the ERNN model comprehensively promote expectile regression.For one thing,the neural network structure can accurately simulate the nonlinear structure through neural network structure.For another,it can reveal the dynamics of the complete conditional distribution of a response variable conditional on covarivates.With this regards,it will have a good prospect of application.