Before revision:  Our computing endeavors starting from encoding events of large return on the original time axis to transform the original return time series into a recurrence-time process on discrete-time-axis. By adopting BIC and clustering analysis, we identify potential multiple volatility states, and then apply the extended HFS algorithm on the recurrence time series to discover its underlying volatility state process. Our decoding approach is found favorably compared with Viterbi's in experiments involving both light and heavy tail distributions.
After revision:  Our computing endeavors starting from encoding events of large return on the original time axis to transform the original return time series is transformed into Bernoulli-variable processes. In the decoding phase, we computationally seek for locations of change points via estimations based on a new searching algorithm conjunction to the Bayesian information criterion applied on the observed collection of recurrence times upon the binary process. Besides the independence required for building the Geometric distributional likelihood function, the proposed approach can functionally partition the entire return time series into a collection of homogeneous segments without any assumptions of dynamic structure and underlying distributions. In the numerical experiments, our approach is found favorably compared with Viterbi's in experiments involving both light and heavy tail distributions.