  We have developed a statistical technique to test the model assumption of
binary regime switching extension of the geometric Brownian motion (GBM) model
by proposing a new discriminating statistics. Given a time series data, we have
identified an admissible class of the regime switching candidate models for the
statistical inference. By performing several systematic experiments, we have
successfully shown that the sampling distribution of the test statistics
differs drastically, if the model assumption changes from GBM to Markov
modulated GBM, or to semi-Markov modulated GBM. Furthermore, we have
implemented this statistics for testing the regime switching hypothesis with
Indian sectoral indices.
