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Volatility of financial stock is referring to the degree of uncertainty orrisk embedded within a stock's dynamics. Such risk has been received hugeamounts of attention from diverse financial researchers. By following theconcept of regime-switching model, we proposed a non-parametric approach, namedencoding-and-decoding, to discover multiple volatility states embedded within adiscrete time series of stock returns. The encoding is performed across theentire span of temporal time points for relatively extreme events with respectto a chosen quantile-based threshold. As such the return time series istransformed into Bernoulli-variable processes. In the decoding phase, wecomputationally seek for locations of change points via estimations based on anew searching algorithm in conjunction with the information criterion appliedon the observed collection of recurrence times upon the binary process. Besidesthe independence required for building the Geometric distributional likelihoodfunction, the proposed approach can functionally partition the entire returntime series into a collection of homogeneous segments without any assumptionsof dynamic structure and underlying distributions. In the numericalexperiments, our approach is found favorably compared with parametric modelslike Hidden Markov Model. In the real data applications, we introduce theapplication of our approach in forecasting stock returns. Finally, volatilitydynamic of every single stock of S&P500 is revealed, and a stock network isconsequently established to represent dependency relations derived throughconcurrent volatility states among S&P500.

Unraveling S&P500 stock volatility and networks -- An encoding-and-decoding approach