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SUMMARY:Information Measure for Long Range Correlated Time Series
DTSTART;VALUE=DATE-TIME:20210702T150900Z
DTEND;VALUE=DATE-TIME:20210702T151000Z
DTSTAMP;VALUE=DATE-TIME:20240806T150206Z
UID:indico-contribution-229@indico.fis.agh.edu.pl
DESCRIPTION:Speakers: Pietro Murialdo (Politecnico di Torino)\nWe applied
the moving average cluster entropy to study long-range correlation\, dynam
ics and heterogeneity of financial time series\, and to propose an alterna
tive method to portfolio estimation.\n\nThe cluster entropy relies on the
Shannon entropy $S(P_i) = - \\sum_i P_i \\ln P_i$. The probability distrib
ution function of each asset $i$ is obtained intersecting the asset time s
eries $y(t)$ with its moving average series $y_n(t)$. The portion of time
series between two consecutive intersections of $y(t)$ and $y_n(t)$ is def
ined as a cluster. Then\, $P(\\tau\,n)$\, which associates clusters of dur
ation $\\tau$ to their frequency\, is fed into the Shannon entropy to obta
in the moving average cluster entropy. We summarize the results into the c
luster entropy index $I(n)$\, obtained integrating $S(\\tau\,n)$ over dura
tion $\\tau$.\n\nWe used high frequency financial time series of important
market indexes (NASDAQ\, DJIA\, S\\&P500\, ...) of 2018. To study their d
ynamics\, we analyzed twelve consecutive temporal horizon\, summing up to
a whole year. \n\nWe found positive long-range correlation for financial d
ata\, similar to fractional stochastic process with Hurst exponent $0.5\\l
eq H\\leq 1$.\nMoreover\, we compared our results to Kullback-Leibler entr
opy results based on the pricing kernel simulations for different represen
tative agent models.\n\nWe show that the cluster entropy of volatility ser
ies depends on the individual asset\, while the cluster entropy of price s
eries is invariant for different assets. Furthermore\, we propose the clus
ter entropy portfolio. Portfolio weights are obtained from the cluster ent
ropy index $I$. We also integrated horizon dependence. We show the cluster
entropy portfolio ability to adjust to market dynamics by varying asset a
llocation.\n\nhttps://indico.fis.agh.edu.pl/event/69/contributions/229/
LOCATION:ONLINE
URL:https://indico.fis.agh.edu.pl/event/69/contributions/229/
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