中文摘要：

本文分析一个转换函数为logistic形式的双阀值平滑转换自回归（LSTAR）模型，并对该模型的非线性进行了诊断检验．通过泰勒展开等手段，用一个简单的线性模型逼近非常复杂的非线性的双阀值LSTAR模型，对应的两个模型的零假设被证明完全等价，从而大大简化模型线性性的诊断检验工作．理论研究表明，不同于单阀值STAR模型需要对转换函数进行三阶泰勒展开，双阀值模型只需要对转换函数进行一阶泰勒展开即可，这大大节省了自由度．模拟研究和实际数据分析结果验证了理论结果的有用性．

英文摘要：

The paper studies testing for the nonlinearity of a LSTAR model based on the transformed function with logistic form. Specifically, a simple linear model can be used to approximate the LSTAR model by Taylor expansion. For the two different models, the null hypothesis has been verified to be equivalent and then the corresponding hypothesis test can be more easily carried out. The research on its nonlinearity testing shows that to test the nonlinearity of this kind of LSTAR models, we need only replace the transition function with its first-order Taylor approximation, which can help us save many degrees of freedom. Monte Carlo simulation studies and real data applications show the usefulness of these theory results.