We extend the Hierarchical Factor Segmentation(HFS) algorithm for discovering multiple volatility states process hidden within each individual S P500 stock's return time series. Then we develop an associative measure to link stocks into directed networks of various scales of associations. Such networks shed lights on which stocks would likely stimulate or even promote, if not cause, volatility on other linked stocks. 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 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. Consequently, we establish data-driven associative networks for S &P500 stocks to discover their global dependency relational groupings with respect to various strengths of links .
 Volatility of financial stock is referring to the degree of uncertainty or risk embedded within a stock's dynamics. Such risk has been received huge amounts of attention from diverse financial researchers. By following the concept of regime-switching model, we proposed a non-parametric approach, named encoding-and-decoding, to discover multiple volatility states embedded within a discrete time series of stock returns. The encoding is performed across the entire span of temporal time points for relatively extreme events with respect to a chosen quantile-based threshold. As such the 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 under Hidden Markov Model (HMM) settings. In the real data applications, volatility dynamics of every single stock of S P500 are computed and revealed. Then, a non-linear dependency of any stock-pair is derived by measuring through concurrent volatility states . Finally, various networks dealing with distinct financial implications are consequently established to represent different aspects of global connectivity among all stocks in S &P500 .
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We extend the Hierarchical Factor Segmentation(HFS) algorithm for discovering multiple volatility states process hidden within each individual S
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P500
Volatility of financial stock is referring to the degree of uncertainty or risk embedded within a
R
return time series. Then we develop an associative measure to link stocks into directed networks of various scales of associations. Such networks shed lights on which stocks would likely stimulate or even promote, if not cause, volatility on other linked stocks. Our computing endeavors starting from encoding events of large return on the original time axis to transform the original
dynamics. Such risk has been received huge amounts of attention from diverse financial researchers. By following the concept of regime-switching model, we proposed a non-parametric approach, named encoding-and-decoding, to discover multiple volatility states embedded within a discrete time series of stock returns. The encoding is performed across the entire span of temporal time points for relatively extreme events with respect to a chosen quantile-based threshold. As such the
R
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
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
R
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
under Hidden Markov Model (HMM) settings. In the real data applications, volatility dynamics of every single stock of S
A
P500 are computed and revealed. Then, a non-linear dependency of any stock-pair is derived by measuring through
R
upon a chosen window. Consequently, we establish data-driven associative networks for S
. Finally, various networks dealing with distinct financial implications are consequently established to represent different aspects of global connectivity among all stocks in S
D
stocks to discover their global dependency relational groupings with respect to various strengths of links