Nonparametric And Semiparametric Additive Model And Its Applications

The fluctuation of the stock market has always been widely concerned.As an important tool for portraying the fluctuation of the stock market,volatility is also a worldwide research hotspot.Currently studies on volatility are mainly based on the GARCH model,but with the introduction of the conditional autoregressive range(CARR)model,related research has pointed out that range can describe the fluctuation of the stock market better.Current research of the CARR model is mostly based on the parameter CARR model.At the same time,some scholars propose the nonparametric CARR model,which is known for its flexibility and has been proved to be more reliable describing the volatility of the stock market.But it is always accompanied by “the disaster of dimension”,which means that the nonparametric CARR model is not an optimal choice when the CARR model has multidimensional independent variables.In view of this,this paper introduces the idea of nonparametric additive model into the CARR model and proposes the nonparametric additive CARR model and its estimation method based on P-spline.Secondly,in order to make up for the nonparametric additive CARR model's weakness of explanatory ability,this paper proposes the semiparametric additive CARR model and its estimation method with reference to the idea of semiparametric additive model.then,compare the estimation results of the parameter CARR model,the nonparametric CARR model,the nonparametric additive CARR and the semiparametric additive CARR model with different lags by data simulation.The result shows that the estimation error of the nonparametric CARR model will increase significantly with increasing lags,while the nonparametric additive CARR model and the semiparametric additive CARR model have better estimation performance in multidimensional situations.Finally,several kinds of CARR models with different lags are applied to worldwide financial markets.The result shows that the nonparametric additive CARR(2,2)model has best estimation accuracy,and the estimation error of the nonparametric CARR(1,1)model,the nonparametric additive CARR(1,1)model and the semiparametric additive CARR(1,1)model is relatively close,while the estimation error of the nonparametric CARR(2,2)model is obviously larger than the nonparametric additive CARR(2,2)model and the semiparametric additive CARR(2,2)model,which indicate that the nonparametric additive CARR model and the semiparametric additive CARR model can describe the stock market fluctuations with multidimensional effects better.