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A Geometric Analysis of Time Series Leading to Information Encoding and a New Entropy Measure. (arXiv:1810.05900v1 [cs.IT])

来源于:arXiv
A time series is uniquely represented by its geometric shape, which also carries information. A time series can be modelled as the trajectory of a particle moving in a force field with one degree of freedom. The force acting on the particle shapes the trajectory of its motion, which is made up of elementary shapes of infinitesimal neighborhoods of points in the trajectory. It has been proved that an infinitesimal neighborhood of a point in a continuous time series can have at least 29 different shapes or configurations. So information can be encoded in it in at least 29 different ways. A 3-point neighborhood (the smallest) in a discrete time series can have precisely 13 different shapes or configurations. In other words, a discrete time series can be expressed as a string of 13 symbols. Across diverse real as well as simulated data sets it has been observed that 6 of them occur more frequently and the remaining 7 occur less frequently. Based on frequency distribution of 13 configuratio 查看全文>>