  A perspective is taken on the intangible complexity of economic and social
systems by investigating the underlying dynamical processes that produce, store
and transmit information in financial time series in terms of the
\textit{moving average cluster entropy}. An extensive analysis has evidenced
market and horizon dependence of the \textit{moving average cluster entropy} in
real world financial assets. The origin of the behavior is scrutinized by
applying the \textit{moving average cluster entropy} approach to long-range
correlated stochastic processes as the Autoregressive Fractionally Integrated
Moving Average (ARFIMA) and Fractional Brownian motion (FBM). To that end, an
extensive set of series is generated with a broad range of values of the Hurst
exponent $H$ and of the autoregressive, differencing and moving average
parameters $p,d,q$. A systematic relation between \textit{moving average
cluster entropy}, \textit{Market Dynamic Index} and long-range correlation
parameters $H$, $d$ is observed. This study shows that the characteristic
behaviour exhibited by the horizon dependence of the cluster entropy is related
to long-range positive correlation in financial markets. Specifically, long
range positively correlated ARFIMA processes with differencing parameter $
d\simeq 0.05$, $d\simeq 0.15$ and $ d\simeq 0.25$ are consistent with
\textit{moving average cluster entropy} results obtained in time series of
DJIA, S\&P500 and NASDAQ.
