单位根模型的复合分位数自回归推断

Composite quantile autoregression inference for the unit root model

单位根模型是经济学和金融学中用于非平稳时间序列数据建模的一个重要模型.对于该模型,假设模型误差的方差可能不存在,然后采用复合分位数方法估计该模型的自回归系数,建立了估计量的收敛速度和极限分布.然后,通过MonteCarlo模拟评估估计量在有限样本情形下的表现发现,当模型误差不是高斯分布时,单位根模型的复合分位数自回归估计在估计偏差和有效性方面要优于最小二乘估计和分位数自回归估计.此外,文中给出了一个相关的实证分析,该实证分析表明:对于该经济数据,用复合分位数方法进行统计推断是合适且具有一定优势的.最后,把单位根模型推广到了增广的Dickey-Fuller模型,并研究了该模型中的复合分位数自回归估计的渐近理论.

The unit root model is an important one for modelling non-stationary time series data in economics and finance.For this model,assuming the innovations may have infinite variances,the composite quantile autoregressive method is used to estimate the autoregressive coefficient in this model,and the consistency as well as the limiting distribution of the estimator are established.Monte Carlo simulations are conducted to examine the finite sample performance for the estimator.It is showed that the composite quantile autoregressive method enjoys greater advantages than both the least squares method and the quantile autoregressive method in terms of estimation bias and estimation efficiency when the innovations depart from Gaussian conditions.In addition,an empirical study is given in this paper to illustrate the applications of the theoretical result.This empirical study shows that the composite quantile autoregressive method is good and enjoys some advantages for this economic data.The augmented Dickey-Fuller model is also studied and the corresponding asymptotic theory for the composite quantile autoregression estimator is also established in this paper.