双阀值LSTAR模型及其非线性检验

The LSTAR Model with Two Thresholds and Its Test of Nonlinearity

本文首先简要介绍了平滑转换回归模型(STR)的含义和检验其非线性的程序,然后以汇率均值回复问题为例说明目前流行的单阀值STR模型有其局限性,存在研究双阀值STR模型的必要。为此,本文对双阀值LSTAR模型的非线性检验进行了分析。结果表明,不同于单阀值STAR模型需要对转换函数进行三阶Taylor展开,双阀值LSTAR模型只需对转换函数进行一阶展开即可,因此大大节省了自由度。

The paper firstly gave a brief introduction to the STR model and provided the procedure to test its nonlinearity.Then,as the mean reversion of exchange rate for example,the paper pointed out that the popular STR model with only one threshold is limited,and that we should begin to study the STR model with two thresholds.So,the paper analyzed the nonlinearity of LSTAR model with two thresholds.The conclusion is that：to test the nonlinearity of this kind of LSTAR models,we need only replace the transition function by its first-order Taylor approximation,which can help us save many degrees of freedom.