Self-weighted M-estimators For Random Coefficient Autoregressive Models

Time series,also known as dynamic data,refers to a set of chronological se-quence of numbers,such as the price index fluctuations in the record,the mechanical system of vibration sequence,and so on.Time series analysis is using stochastic process theory and mathematical statistical method,based on times seris data,to study the statistical laws for solving practical problems.However,the real world of things is often non-linear,which implies that the use of nonlinear model is more appropriate.Random coeffcient autoregressive time series(RCA)model,where the coefcients of the RCA model are randomly fluctuated,is a promotion of autoregressive time series and a nonlinear model.This paper mainly investigtes the expectation and variance of the random coefficient in RCA(1)models.Due to time series data often have abnormal points and heavy tail property,the commonly used least squares estimation is not robust enough and LAD estimates can not eliminate the effects of high leverage points.For robustness,we construct the self-weighted M-estimator of random coefficient expect,ation and the asymptotic normality is proved under certain conditions.At the same time,the advantage of the self-weighted M-estimator is verifed by numerical simulation,as well as an empirical data analysis,and its asymptotic normal state is also exhibited.At last,we construct the self-weighted M-estimator of the random coeffcient variance.Note that the random coeffcient may have some correlation with the interference term,and thus it is necessary to estimate the disturbance term,the random coeffcient expectation and the variance of the random coefcient.In this paper,the estimator limit distributions are given by theoretical proof.In addition,a numerical simulation shows the self-weighted M-estimators of variance are more effective than ordinary least squares estimates.