Before revision:  Our decoding approach is found favorably compared with Viterbi's in experiments involving both light and heavy tail distributions. After recovering the volatility state process back to the original time-axis, we decode and represent stock dynamics of each stock . Our measurement of association is measured through overlapping  concurrent volatility states upon a chosen window.
After revision:  Our decoding approach is found favorably compared with Viterbi's under Hidden Markov Model (HMM) settings. In the real data applications, volatility dynamics of every single stock of S concurrent volatility states upon a chosen window.