Quantile Inference Of Nonlinear Autoregressive Model

As the movement law of the real world is often nonlinear,the nonlinear time series model has been widely concerned and applied in recent decades.This paper mainly considers the nonlinear autoregressive model of xt = f(xt-1,xt-2,…,xt-p,?)??t,which contains a series of commonly used models(see Tong,Fan&Yao).In the literature on the above-mentioned nonlinear autoregressive model,the parameter estimation methods involved in ? are mostly least squares estimation or median estimation(L1).It is well known that the least squares estimation is suscep-tible to exception value and heavy-tailed data so that is not robust;Ll estimation is robust,but there is a common drawback to least squares estimation,which is to study only the effect of explanatory variables on the average level of response vari-ables,and in many cases(such as the liquidity between the stock market and the financial risk of the financial market),it is often necessary to study the tail charac-teristics of the variables.In view of this,we construct the quantile estimation of ?and the asymptotic normality of the estimator is proved under certain conditions.At the same time,random stochastic simulation is carried out under the conditions of stochastic disturbance items,such as standard normal distribution,t(3)distri-bution and mixed normal distribution,which indicates that the quantile estimation is robust and effective.It is well known that the financial time series data often have the characteristics of spikes and thick tails,which means the variance of the data is large and even infinite.While in the proof of the quantile estimation,the variance of the random perturbation is limited,which limits the scope of application of the model.In view of this,we construct the self-weighted quantile estimation.The asymptotic normality of the estimator is proved under the condition that the variance of the random perturbation term is infinite.And the stochastic simulation is carried out under the condition that the random perturbation subjects to t(2)distribution and Cauchy distribution,which shows that the self-weighted quantile estimation is more effective than the quantile estimation.