带高次趋势项的ADF单位根检验

ADF Unit Root Test with High Order Trend Term

研究目标:探讨带高次趋势项的ADF单位根检验。研究方法:构造了带高次趋势项ADF检验中的单位根检验、联合F检验和高次趋势项系数检验的统计量,推导了其渐近分布;用蒙特卡罗仿真获得了渐近分布的临界值。研究发现:本文的讨论涵盖了传统ADF检验的三种情形,发现单位根检验的渐近分布可表示为统一的函数形式。仿真发现,单位根检验和联合F检验的渐近分布分别向左和向右平移,高次趋势项系数检验的渐近分布向两侧延伸,且随趋势项阶数增加,平移幅度增大,延伸幅度缓慢增大。研究创新:改进了传统ADF检验,提出了针对含高次趋势序列的单位根检验方法。研究价值:扩展单位根检验在高次趋势方面的理论,为含高次趋势序列平稳性分析提供理论支持。

Research Objectives: This paper explores the ADF unit root test with high order trend term.Research Methods: This paper has constructed the test statistics of unit root test, joint F test and high order trend term coefficient test in ADF unit root test with high order trend term.The asymptotic distribution of these three test statistics is derived then.Finally, their critical values are obtained by Monte Carlo simulationResearch Findings: The test in this paper are conducted in the three test types in traditional ADF unit root test, it is found that the asymptotic distribution of unit root test can be expressed as an uniform function.Monte Carlo Simulation results indicate that the asymptotic distribution of unit root test and joint F test shifts left and right respectively, the asymptotic distribution of high order trend term coefficient test extends to both sides.With the increase of the trend term's order, the range of the asymptotic distribution's shift increases and that of the asymptotic distribution's extension increases slowly.Research Innovations: The traditional ADF unit root test has been improved and a new unit root test method which can be used for the test of series with high order trend is proposed.Research Value: This paper extends the theory of unit root test in high order trend and provides theoretical support of stationary analysis of series with high order trend.