广义Breitung非参数单位根检验研究——基于平稳假设下序列长期方差一致估计的分析

A Study of Generalized Breitung Nonparametric Unit Root Test

Breitung检验中生成序列的误差项的自相关会影响有限样本性质。本文用平稳假设下序列长期方差的一致估计量作为统计量的分母对其进行了修正。给出了修正后的统计量及其渐近理论,并对修正前后的有限样本性质进行了仿真。结果显示,修正后统计量概率密度的左偏有所减少;当误差项有自相关时,修正后检验的水平扭曲有所改进;当样本较小时,随误差项自回归(移动平均)系数或序列自回归系数的增加,修正后检验的势逐渐大于Breitung检验的势。

In Breitung＇s test, the autocorrelation of the error term used to gen- erate the series has an affect on the Finite Sample Properties. This paper, using the consistent estimator of series＇ Long Run Variance under stationary hypothesis as the denominator of test＇s statistic, corrects Breitung＇s test. In this paper, the cor- rected test statistic and its asymptotic theory are introduced, firstly. And then, the Finite Sample Properties of corrected and non-corrected test are compared by Monte Carlo Simulation. The results show that, compared with the non-corrected test, the corrected test reduces the left skewness of statistics＇ probability density. When error term is auto-correlated, the corrected test has some improvement in test＇s size distortion. When sample size is small, along with the increase of error term＇s au- toregressive （moving average） coefficient and series＇ autoregressive coefficient, the empirical power of corrected test becomes greater than that of non-corrected test gradually.