Statistical Inference Of Several Classes Of Semiparametric Autoregressive Models

Many economic laws have a dependency relationship,which can be described by a time series model.In addition to the dependency relationship,these data are also affected by other factors,and sometimes show a nonlinear relationship.Empirical research shows that semi-parametric autoregressive models can fit such data better than traditional linear regression.Therefore,a semiparametric autoregressive model with nonlinear explanatory variables came into being.This paper presents a class of semiparametric additive autoregressive models,considers the estimation of model parameters and nonlinear functions,and applies the model to the empirical analysis of gold price data.In order to characterize the asymmetry and threshold characteristics of time series data,a type of semiparametric threshold autoregressive model is proposed,and numerical algorithms for estimating the parameters and nonlinear functions of the model are given.The effectiveness of the estimation is verified by numerical simulation,and The proposed model was fitted with the RMB/USD mid-price dataThe main contents of this paper are as follows:In the first part,a class of semiparametric additive autoregressive models is constructed.Based on the conditional least squares method and kernel estimation method,an algorithm for estimating model parameters and unknown functions is given.The asymptotic properties of the estimator are discussed.The estimated value is verified by numerical simulation.Effect,and apply the model to the empirical analysis of gold price data.The empirical analysis results show that the proposed model can better fit the gold price law than the existing model.In the second part,a kind of semiparametric threshold autoregressive model is constructed.The threshold parameters of the model are estimated based on the single-grid search method,and the unknown parameters and unknown functions of the model are estimated using the method proposed earlier in this paper.The effect of the estimation is verified by numerical simulation and the The model is applied to the empirical analysis of the RMB/USD mid-price data.The results of the empirical analysis show that the proposed model can better fit the RMB/USD mid-price data than the existing models.