整数值时间序列模型单位根检验问题研究

Research on Unit Root Test for Integer-valued Time Series Models

非整数值时间序列单位根检验研究已趋成熟,而整数值时间序列单位根检验则刚起步。本文主要采用蒙特卡洛模拟方法对INAR（1）模型单位根检验中的DF统计量和∑ ^Tt= 1{ΔXt〈0}统计量进行了研究。研究发现：DF统计量渐近服从标准正态分布,有限样本情形下,该统计量的实际分布会受到样本容量与扰动项均值的影响;DF统计量不存在水平扭曲现象,能很好控制犯第一类错误的概率,由于数据生成特点,∑_t=1~TI{ΔXt〈0}统计量犯第一类错误的概率始终为0;DF统计量和∑_t=1~TI{ΔXt〈0}统计量的检验功效受到样本容量、自回归系数和扰动项均值的影响,多数情形下,∑_t=1~TI{ΔXt〈0}统计量的检验功效高于DF统计量。

The unit root test research about the integer-valued time series is just getting started, compared with the non-integer-valued time series. In this paper, the Monte Carlo simulation would be ushered to check the DF statistic and the ∑ ^Tt= 1{ΔXt〈0} statistic in INAR （1） models with unit root process. Based on the research, DF statisticasymptotically conforms to the standard normal distribution, meanwhile the actual distribution of this statistic has been impacted by the sample size and the mean of the disturbance term in the finite sample. In addition, the DF statistic does not have the property of any level distortion. That is, the DF can well control the probability of type I error. Because of thedata generation feature, the ∑ ^Tt= 1{ΔXt〈0}statistic＇ s probability of committing type I error is zero. Furthermore, thetest powers of DF statistic and∑ ^Tt= 1{ΔXt〈0}statistic are influenced by the sample size, autoregressive coefficient andthe mean of the error term. In most cases, the test power of∑ ^Tt= 1{ΔXt〈0}statistic is much better than the DFstatistic.