A note on testing regime switching assumption based on recurrence times

By perceiving a regime switching model as an example of a nonlinear dynamical system, we employ recurrence time distribution of a chosen event to derive a test statistic for testing the null hypothesis of one regime versus the alternative of having two or more regimes involved in a time series. This simple chi-square type of statistic is compared with existing likelihood ratio based ones that are all, in general, very complex in construction. The power of our proposed test is rather satisfactory and the computing load required is significantly more economical.