Market dynamic is studied by quantifying the dependence of the entropy S(\tau,n) of the clusters formed by the  series of the prices p_t and its moving average p_{t,n} on temporal horizon M. We report results of the analysis\par  performed on high-frequency data of the Nasdaq Composite, Dow Jones Industrial Avg and Standard \& Poor 500 indexes downloaded from the Bloomberg terminal www. bloomberg.com/professional. Both raw and sampled data series have been analysed for a broad range of horizons M, varying from one to twelve months over the year 2018. A systematic dependence of the cluster entropy function S(\tau,n) on the horizon M has been evidenced in the analysed assets. Hence, the cluster entropy function is integrated over the cluster  \tau to yield a synthetic indicator of price evolution: the\emph{Market Dynamic Index I(M,n) . Moreover, the\emph{Market Horizon Dependence\par   defined as H(M,n)=I(M,n)-I(1,n) is calculated and compared with the values of the horizon dependence of the pricing kernel with different representative agent models obtained by a Kullback-Leibler entropy approach  .
Market dynamic is quantified in terms of the entropy S(\tau,n) of the clusters formed by the intersections between the series of the prices p_t and the moving average p_{t,n} . The entropy S(\tau,n) is defined according to Shannon as \sum P(\tau,n)\log P(\tau,n), with P(\tau,n) the probability for the cluster to occur with duration \tau.\par The investigation is performed on high-frequency data of the Nasdaq Composite, Dow Jones Industrial Avg and Standard \& Poor 500 indexes downloaded from the Bloomberg terminal . The cluster entropy S(\tau,n) is analysed in raw and sampled data over a broad range of temporal horizons M varying from one to twelve months over the year 2018. The cluster entropy S(\tau,n) is integrated over the cluster duration \tau to yield \emph{the Market Dynamic Index I(M,n), a synthetic figure of price dynamics. A systematic dependence of the cluster entropy S(\tau,n) and the Market Dynamic Index I(M,n) \emph{on the temporal horizon M is evidenced.\par Finally, the Market Horizon Dependence , defined as H(M,n)=I(M,n)-I(1,n) , is compared with the horizon dependence of the pricing kernel with different representative agents obtained via a Kullback-Leibler entropy approach . The Market Horizon Dependence H(M,n) of the three assets is compared against the values obtained by implementing the cluster entropy S(\tau,n) approach on artificially generated series (Fractional Brownian Motion) .
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