Composite Quantile Inference For Autoregressive Model

Time series analysis is a commonly used method for statistical analysis,is an important means to explore dynamic evolution of complex system for the real world As a common linear time series model,the autoregressive time series,which shows the current state inform of the linear combination of the past states,is widely used in various fields.Under this background,the research on the autoregressive model of time series has a rapid development in recent decades.autoregressive model under different conditions more and more attracts the attention of economists.This paper focuses on composite quantile inference for "heavy-tailed" autoregressive model.According to the degree that regression coefficient of autoregressive model de-viates 1,the model can be divided into five types:stationary process,almost non-stationary process,unit root process,"moderate deviation" autoregressive process and explosive process.In this paper,we first introduce the "moderate deviation"autoregressive model with infinite variance.Since containing the explosive process that can be to explain price bubble exactly,the model has long drawn many schol-ars' attention since it was put forward in 2006.Based on the model error is normal attraction,composite quantile estimators of regression coefficients are constructed in this paper and the asymptotic distribution of the estimators are proved when the distribut,ion of model error are different(including normal distribution and Cauchy distribution).finally,composite quantile estimator is compared with ordinary least squares estimator and quantile estimator by data simulation.Next,we study an almost nonstationary autoregressive model with infinite variance.Under the condition of heavy-tail that model error belongs to ?-stable field(??(0,2)),composite quantile estimator of regressive coefficient is constructed,and is proved to converge to the Wiener process.At the same time,the results of the random simulation show that composite quantile estimator of the model pa-rameter is more effective than the ordinary least squares estimator and the quantile estimator.