2019/08/01 by Linda Ponta, A. Carbone, Ponta, L. +1
Decision Sciences · Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Computational Finance (q-fin.CP) #Data Analysis #FOS: Economics and business #FOS: Physical sciences #Financial Risk and Volatility Modeling #Innovation Diffusion and Forecasting #Market Dynamics and Volatility #Statistical Finance (q-fin.ST) #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.1908.00257
openalex publication_date 2019/08/01 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
Market dynamic is quantified in terms of the entropy S(\τ,n) of the\nclusters formed by the intersections between the series of the prices pt and\nthe moving average widetildept,n. The entropy S(\τ,n) is defined\naccording to Shannon as \∑ P(\τ,n)\log P(\τ,n), with P(\τ,n) the\nprobability for the cluster to occur with duration \τ. par The\ninvestigation is performed on high-frequency data of the Nasdaq Composite, Dow\nJones Industrial Avg and Standard & Poor 500 indexes downloaded from the\nBloomberg terminal. The cluster entropy S(\τ,n) is analysed in raw and\nsampled data over a broad range of temporal horizons M varying from one to\ntwelve months over the year 2018. The cluster entropy S(\τ,n) is integrated\nover the cluster duration \τ to yield the Market Dynamic Index I(M,n), a\nsynthetic figure of price dynamics. A systematic dependence of the cluster\nentropy S(\τ,n) and the Market Dynamic Index I(M,n) on the temporal\nhorizon M is evidenced. par Finally, the Market Horizon Dependence, defined\nas H(M,n)=I(M,n)-I(1,n), is compared with the horizon dependence of the\npricing kernel with different representative agents obtained via a\nKullback-Leibler entropy approach. The Market Horizon Dependence H(M,n) of\nthe three assets is compared against the values obtained by implementing the\ncluster entropy S(\τ,n) approach on artificially generated series\n(Fractional Brownian Motion).\n