Some comments on Bitcoin market (in)efficiency.

In this paper, we explore the (in)efficiency of the continuum Bitcoin-USD market in the period ranging from mid 2010 to early 2019. To deal with, we dynamically analyse the evolution of the self-similarity exponent of Bitcoin-USD daily returns via accurate FD4 approach by a 512 day sliding window with overlapping data. Further, we define the memory indicator by the difference between the self-similarity exponent of Bitcoin-USD series and the self-similarity index of its shuffled series. We also carry out additional analyses via FD4 approach by sliding windows of sizes equal to 64, 128, 256, and 1024 days, and also via FD algorithm for values of q equal to 1 and 2 (and sliding windows equal to 512 days). Moreover, we explored the evolution of the self-similarity exponent of actual S&P500 series via FD4 algorithm by sliding windows of sizes equal to 256 and 512 days. In all the cases, the obtained results were found to be similar to our first analysis. We conclude that the self-similarity exponent of the BTC-USD (resp., S&P500) series stands above 0.5. However, this is not due to the presence of significant memory in the series but to its underlying distribution. In fact, it holds that the self-similarity exponent of BTC-USD (resp., S&P500) series is similar or lower than the self-similarity index of a random series with the same distribution. As such, several periods with significant antipersistent memory in BTC-USD (resp., S&P500) series are distinguished.

A model for foreign exchange markets based on glassy Brownian systems.

In this work we extend a well-known model from arrested physical systems, and employ it in order to efficiently depict different currency pairs of foreign exchange market price fluctuation distributions. We consider the exchange rate price in the time range between 2010 and 2016 at yearly time intervals and resolved at one minute frequency. We then fit the experimental datasets with this model, and find significant qualitative symmetry between price fluctuation distributions from the currency market, and the ones belonging to colloidal particles position in arrested states. The main contribution of this paper is a well-known physical model that does not necessarily assume the independent and identically distributed (i.i.d.) restrictive condition.

Diffusive and Arrestedlike Dynamics in Currency Exchange Markets.

This work studies the symmetry between colloidal dynamics and the dynamics of the Euro-U.S. dollar currency exchange market (EURUSD). We consider the EURUSD price in the time range between 2001 and 2015, where we find significant qualitative symmetry between fluctuation distributions from this market and the ones belonging to colloidal particles in supercooled or arrested states. In particular, we find that models used for arrested physical systems are suitable for describing the EURUSD fluctuation distributions. Whereas the corresponding mean-squared price displacement (MSPD) to the EURUSD is diffusive for all years, when focusing in selected time frames within a day, we find a two-step MSPD when the New York Stock Exchange market closes, comparable to the dynamics in supercooled systems. This is corroborated by looking at the price correlation functions and non-Gaussian parameters and can be described by the theoretical model. We discuss the origin and implications of this analogy.