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The limited penetrable horizontal visibility algorithm is a new time analysistool and is a further development of the horizontal visibility algorithm. Wepresent some exact results on the topological properties of the limitedpenetrable horizontal visibility graph associated with random series. We showthat the random series maps on a limited penetrable horizontal visibility graphwith exponential degree distribution $P(k)\sim exp[-\lambda (k-2\rho-2)],\lambda = ln[(2\rho+3)/(2\rho+2)],\rho=0,1,2,...,k=2\rho+2,2\rho+3,...$,independent of the probability distribution from which the series wasgenerated. We deduce the exact expressions of the mean degree and theclustering coefficient and demonstrate the long distance visibility property.Numerical simulations confirm the accuracy of our theoretical results. We thenexamine several deterministic chaotic series (a logistic map, theH$\acute{e}$non map, the Lorentz system, and an energy price chaotic system)and a real crude oil price series to test our results. The empirical resultsshow that the limited penetrable horizontal visibility algorithm is direct, hasa low computational cost when discriminating chaos from uncorrelatedrandomness, and is able to measure the global evolution characteristics of thereal time series.

Exact results of the limited penetrable horizontal visibility graph associated to random time series and its application