带趋势项ESTAR模型单位根检验的渐进分布

Asymptotic distribution of unit root test based onESTAR model with trend term

对2种不同形式的带趋势项ESTAR(exponential smooth transition autoregression,指数平滑转换自回归)模型的单位根检验进行研究,基于辅助方程,给出了带趋势项ESTAR模型2种不同形式下KSS(Kapetanios-Shin-Snell)检验统计量的极限分布。通过对比发现,2种带趋势项形式下检验统计量的极限分布并不一致。这一结果表明采用带趋势项ESTAR模型建模前需对这2种形式加以区分,对模型进行单位根检验时,由于极限分布并不一致,不能都采用OLS(ordinary least squares,常规最小二乘法)去趋势的临界值给出检验结果,否则会导致结果不可靠。这为进一步对带确定性趋势项STAR(smooth transition autoregression,平滑转换自回归)模型单位根检验的研究提供了理论参考,也为后续提高带趋势项STAR单位根检验功效提供了新思路。

The unit root test of two different forms of ESTAR(exponential smooth transition autoregression)model with trend term was discussed to figure out the limit distribution of KSS(Kapetanios-Shin-Snell)test statistics under two different forms of ESTAR model with trend term,based on the auxiliary equation.By comparison,it is found that the limit distributions of test statistics are not consistent in the two models with trend terms.This result shows that the two forms need to be distinguished before ESTAR model with trend term is used.Because the limit distribution is not consistent,the conventional OLS(ordinary least squares)detrended critical value cannot be used to give the test results,otherwise the results would be unreliable,which provides theoretical references for further research on unit root test of STAR(smooth transition autoregression)model with deterministic trend and a new way to further improve the power of STAR unit root test with trend term.