Research On Reducing Dimensionality Of The Nonparametric And Semiparametric Conditional Covariance Matrix Models

In the background of the rapid development of science and technology,the rise of big data technology has been making people's life more scientific and rational.However,applying the big data needs to deal with a large amount of data information,and the abstraction of information into variables will make the dimensionality of the variables higher,which makes the problem complicated.Reducing dimensionality can effectively optimize the information,and the research of reducing dimensionalit-y will promote the development of big data.The conditional covariance matrix plays an important role in portfolio and financial risk management.Therefore,in the era of big data,it is an important work to study the reducing dimensionality of the high dimensional conditional covariance matrix model,which will expand the application space of the high dimensional covariance matrix model.There are parametric?semiparametric and nonparametric models for estimating the conditional covariance matrix.Parametric models should know exactly functional form and joint density function,but which sometimes is difficult to be known.Otherwise,the nonparametric estimations techniques does not need to know the functional form and joint density function,which can avoid the misspecifications of models.To some extent,the nonparametric model has greater flexibility.The semiparametric models contain the advantages of' both the nonparametric and the parametric models.But the nonparametric and some semiparametric models are subject to the"Curse of dimensionality".In this paper,principal component analysis is used to estimate reducing dimensionality of some nonparametric and some semiparametric models,and then made it possible to be used in conditional covariance matrix.First,the paper researched on the development of univariate and multivariate conditional variance and covariance models,and determined the contents of the research.Secondly,it introduced the theory of principal component analysis and multivariate nonparametric regression estimation,which contributes a theoretical preparation for the new models proposed in this paper.Then,on the basis of the previous research,the nonparametric and semiparametric multivariate conditional covariance models of dimensionality reduction are proposed.Finally,when,according to the proposed new model,we estimate the value at risk with the data of 60 stocks in Hongkong stock market and compare it with the estimated results of several existing multivariate covariance models,We find that the method proposed in this paper outperform others.The innovations of the paper are mainly the following three aspects:firstly,one nonparametric and two semiparametric conditional of reducing dimensionality covariance models is carried out by principal component analysis,which extends the application scope of three covariance models.Secondly,in the case of high dimensionality,the multivariate conditional orthogonal model has been improved,and the nonparametric and semiparametric methods are involved in it.This study relaxed the conditions of multivariate orthogonal covariance model,and would improve the condition of high dimensional covariance model estimation theory.Thirdly,the VaR of 60 stocks portfolio in Hongkong stock market are estimated with the new model proposed in this paper,and then are compared with several covariance models.The result shows that the proposed model outperformed other models.Therefore,the study of this paper also provides a new method for estimating the VaR of the portfolio.The innovations of the paper are mainly the following three aspects:firstly,one nonparametric and two semiparametric conditional of reducing dimensionality covariance models is carried out by principal component analysis,which extends the application scope of three covariance models.Secondly,in the condition of high dimensionality,the multivariate conditional orthogonal model has been improved,the nonparametric and semiparametric methods are applied for estimating,this study relaxed the conditions of multivariate orthogonal covariance model,improving the condition of high dimensional covariance model estimation theory.Thirdly,for the new model proposed in this paper,the value at risk of 60 stocks portfolio in Hongkong stock market are estimated,and the estimation results are compared with several covariance models that can estimate high-dimensional conditional covariance matrixs,we find that the proposed model outperformed other models.So,the study of this paper also provide a new method for estimating the value at risk of the portfolio.