平滑转换自回归模型的平稳性问题研究

根据时间序列宽平稳的定义,本文认为,平滑转换自回归模型的序列不是宽平稳序列,利用ADF统计量检验其平稳性是没有意义的;其次,依据马尔科夫链的遍历性,我们认为,STAR模型的序列是严平稳序列,且通过对模型系数的联合取值的限制保证了模型的平稳性。以一阶对数平滑转换自回归模型为例,其平稳的条件是,β与r符号相反,且|β+r|<1,β可以等于1,也可以绝对值小于1。

Research on the Stationarity of Smooth Transition Autoregressive Model

According to the definition of weakly stationary sequence,we consider that the sequence of smooth transition autoregressive model is not weakly stationary,and using the ADF statistic to test its stationarity makes no sense.Furthermore,based on Markov Chain ergodicity,we believe that the STAR model sequence is strictly stationary,and the joint limit of the model coefficients value ensures the stationarity of the model.Using the first order logarithmic STAR model as example,its stationary condition isβ+r<1,while β can be equal to 1 and the absolute value can also be less than 1.