arXiv subjects
Publications and source records attributed to F. N. M. de Sousa Filho.
In a recent Letter [1] a framework for estimating entropy was introduced and applied to one-dimensional and two-dimensional systems. In this Comment we show that the method is not well suited for estimating entropy in bidimensional systems presenting long-range correlations.
We investigate the performance of entropy estimation methods, based either on block entropies or compression approaches, in the case of bidimensional sequences. We introduce a validation dataset made of images produced by a large number of different natural systems, in the vast majority characterized by long-range correlations, which produce a large spectrum of entropies. Results show that the framework based on lossless compressors applied to the one-dimensional projection of the considered dataset leads to poor estimates. This is because higher-dimensional correlations are lost in the projection operation. The adoption of compression methods which do not introduce dimensionality reduction improves the performance of this approach. By far, the best estimation of the asymptotic entropy is generated by the faster convergence of the traditional block-entropies method. As a by-product of our analysis, we show how a specific compressor method can be used as a potentially interesting technique for automatic detection of symmetries in textures and images.
In this work, we develop a general method for estimating the Shannon entropy of a bidimensional sequence based on the extrapolation of block entropies. We apply this method to analyse the spatial configurations of cities of different cultures and regions of the world. Findings suggest that this approach can identify similarities between cities, generating accurate results for recognising and classifying different urban morphologies. The hierarchical clustering analysis based on this metric also opens up new questions about the possibility that urban form can embody characteristics related to different cultural identities, historical processes and geographical regions.
In this paper, we explore some stylized facts of the Bitcoin market using the BTC-USD exchange rate time series of historical intraday data from 2013 to 2020. Bitcoin presents some very peculiar idiosyncrasies, like the absence of macroeconomic fundamentals or connections with underlying assets or benchmarks, an asymmetry between demand and supply and the presence of inefficiency in the form of strong arbitrage opportunity. Nevertheless, all these elements seem to be marginal in the definition of the structural statistical properties of this virtual financial asset, which result to be analogous to general individual stocks or indices. In contrast, we find some clear differences, compared to fiat money exchange rates time series, in the values of the linear autocorrelation and, more surprisingly, in the presence of the leverage effect. We also explore the dynamics of correlations, monitoring the shifts in the evolution of the Bitcoin market. This analysis is able to distinguish between two different regimes: a stochastic process with weaker memory signatures and closer to Gaussianity between the Mt. Gox incident and the late 2015, and a dynamics with relevant correlations and strong deviations from Gaussianity before and after this interval.