2015/03/19 by William J. Ralph, Ralph, William J.
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Econometrics #Economics #Entropy (arrow of time) #FOS: Mathematics #Finance #Financial Risk and Volatility Modeling #Mathematics #Random variable #Reciprocal #Statistic #Statistical Mechanics and Entropy #Statistics #Statistics Theory (math.ST) #Summary statistics #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1503.05629
6 figures. arXiv admin note: substantial text overlap with arXiv:1404.4339
arxiv created 2015/03/19 · openalex publication_date 2015/03/19 · arxiv updated 2015/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new approach to financial returns based on an infinite family of statistics called slide statistics. The evidence these statistics provide suggests that certain distributions such as the stable distributions are not good models for the financial returns from various securities and indexes. The slide statistics are derived from a variant of differential entropy called the genial entropy and can be computed for any sample in a metric space. We give explicit formulas for the first two of these statistics that are easily evaluated by a computer and make this theory particularly suitable for applications. In simulations with a normal random variable, the first slide statistic appears to converge to Pi/4 and for certain other random variables it appears to converge to the reciprocal of the Hausdorff dimension.