Information-theoretic measures for nonlinear causality detection: application to social media sentiment and cryptocurrency prices.

Information transfer between time series is calculated using the asymmetric information-theoretic measure known as transfer entropy. Geweke's autoregressive formulation of Granger causality is used to compute linear transfer entropy, and Schreiber's general, non-parametric, information-theoretic formulation is used to quantify nonlinear transfer entropy. We first validate these measures against synthetic data. Then we apply these measures to detect statistical causality between social sentiment changes and cryptocurrency returns. We validate results by performing permutation tests by shuffling the time series, and calculate the Z-score. We also investigate different approaches for partitioning in non-parametric density estimation which can improve the significance. Using these techniques on sentiment and price data over a 48-month period to August 2018, for four major cryptocurrencies, namely bitcoin (BTC), ripple (XRP), litecoin (LTC) and ethereum (ETH), we detect significant information transfer, on hourly timescales, with greater net information transfer from sentiment to price for XRP and LTC, and instead from price to sentiment for BTC and ETH. We report the scale of nonlinear statistical causality to be an order of magnitude larger than the linear case.

Peer-to-peer loan acceptance and default prediction with artificial intelligence.

Logistic regression (LR) and support vector machine algorithms, together with linear and nonlinear deep neural networks (DNNs), are applied to lending data in order to replicate lender acceptance of loans and predict the likelihood of default of issued loans. A two-phase model is proposed; the first phase predicts loan rejection, while the second one predicts default risk for approved loans. LR was found to be the best performer for the first phase, with test set recall macro score of 77.4 % . DNNs were applied to the second phase only, where they achieved best performance, with test set recall score of 72 % , for defaults. This shows that artificial intelligence can improve current credit risk models reducing the default risk of issued loans by as much as 70 % . The models were also applied to loans taken for small businesses alone. The first phase of the model performs significantly better when trained on the whole dataset. Instead, the second phase performs significantly better when trained on the small business subset. This suggests a potential discrepancy between how these loans are screened and how they should be analysed in terms of default prediction.

Asymptotic scaling properties and estimation of the generalized Hurst exponents in financial data.

We propose a method to measure the Hurst exponents of financial time series. The scaling of the absolute moments against the aggregation horizon of real financial processes and of both uniscaling and multiscaling synthetic processes converges asymptotically towards linearity in log-log scale. In light of this we found appropriate a modification of the usual scaling equation via the introduction of a filter function. We devised a measurement procedure which takes into account the presence of the filter function without the need of directly estimating it. We verified that the method is unbiased within the errors by applying it to synthetic time series with known scaling properties. Finally we show an application to empirical financial time series where we fit the measured scaling exponents via a second or a fourth degree polynomial, which, because of theoretical constraints, have respectively only one and two degrees of freedom. We found that on our data set there is not clear preference between the second or fourth degree polynomial. Moreover the study of the filter functions of each time series shows common patterns of convergence depending on the momentum degree.

Spread of risk across financial markets: better to invest in the peripheries.

Risk is not uniformly spread across financial markets and this fact can be exploited to reduce investment risk contributing to improve global financial stability. We discuss how, by extracting the dependency structure of financial equities, a network approach can be used to build a well-diversified portfolio that effectively reduces investment risk. We find that investments in stocks that occupy peripheral, poorly connected regions in financial filtered networks, namely Minimum Spanning Trees and Planar Maximally Filtered Graphs, are most successful in diversifying, improving the ratio between returns' average and standard deviation, reducing the likelihood of negative returns, while keeping profits in line with the general market average even for small baskets of stocks. On the contrary, investments in subsets of central, highly connected stocks are characterized by greater risk and worse performance. This methodology has the added advantage of visualizing portfolio choices directly over the graphic layout of the network.

Building complex networks with Platonic solids.

We propose a unified model to build planar graphs with diverse topological characteristics which are of relevance in real applications. Here convex regular polyhedra (Platonic solids) are used as the building blocks for the construction of a variety of complex planar networks. These networks are obtained by merging polyhedra face by face on a tree-structure leading to planar graphs. We investigate two different constructions: (1) a fully deterministic construction where a self-similar fractal structure is built by using a single kind of polyhedron which is iteratively attached to every face and (2) a stochastic construction where at each step a polyhedron is attached to a randomly chosen face. These networks are scale-free, small-world, clustered, and sparse, sharing several characteristics of real-world complex networks. We derive analytical expressions for the degree distribution, the clustering coefficient, and the mean degree of nearest neighbors showing that these networks have power-law degree distributions with tunable exponents associated with the building polyhedron, and they possess a hierarchical organization that is determined by planarity.

Specific surface area and volume fraction of the cherry-pit model with packed pits.

This paper investigates volume fraction phi and specific surface area s for statistically homogeneous systems of partially penetrating spheres, i.e. so-called 'cherry-pit models'. In contrast to the version where the pits form an equilibrium system of hard spheres, here pits or hard spheres are considered which are packed, can be in direct contact, and form a nonequilibrium distribution. For this kind of system, new formulas for phi and s are given, which yield values in good agreement with the ones for large models constructed from hard sphere packings generated both experimentally and numerically. Surprisingly, the existing formulas for phi and s in the equilibrium cherry-pit model lead to values which deviate substantially from the values obtained here.

Structural and entropic insights into the nature of the random-close-packing limit.

Disordered packings of equal sized spheres cannot be generated above the limiting density (fraction of volume occupied by the spheres) of rho approximately 0.64 without introducing some partial crystallization. The nature of this "random-close-packing" limit (RCP) is investigated by using both geometrical and statistical mechanics tools applied to a large set of experiments and numerical simulations of equal-sized sphere packings. The study of the Delaunay simplexes decomposition reveals that the fraction of "quasiperfect tetrahedra" grows with the density up to a saturation fraction of approximately 30% reached at the RCP limit. At this limit the fraction of aggregate "polytetrahedral" structures (made of quasiperfect tetrahedra which share a common triangular face) reaches it maximal extension involving all the spheres. Above the RCP limit the polytetrahedral structure gets rapidly disassembled. The entropy of the disordered packings, calculated from the study of the local volume fluctuations, decreases uniformly and vanishes at the (extrapolated) limit rho(Kappa) approximately 0.66 . Before such limit, and precisely in the range of densities between 0.646 and 0.66, a phase separated mixture of disordered and crystalline phases is observed.

Emergence of Gamma distributions in granular materials and packing models.

We study the distribution of volume fluctuations in experiments and numerical simulations concerning equal-sized sphere packings prepared with different techniques. We show that the distribution of the local volumes (Voronoï cells) and also the distributions of the global volumes (whole samples) follow remarkably well a shifted and rescaled Gamma distribution that we name a k-Gamma distribution. Such agreement is robust over a broad range of packing fractions and it is observed for several distinct systems. This distribution is characterized by the average packing fraction and a shape parameter "k" which is very sensitive to changes in the structural organization. A statistical mechanics approach predicts such k-Gamma distribution at statistical equilibrium and it links the parameter k with the number of elementary cells which are exchanging volume during the system preparation. The thermodynamical equivalent of k and its relation with the "granular temperature" are also discussed.

Correlations and aggregate statistics in granular packs.

We study how the aggregate statistical properties for density fluctuations in granular aggregates scale with the sample size and how such a scaling is associated with the correlations between grains. Correlations are studied both between grain positions and between Voronoï cell volumes, showing distinct behaviors and properties. A non-linear scaling in the aggregate volume fluctuations as function of the sample size is discovered and the connection between such anomalous scaling and correlations is explained. It emerges that volume fluctuations might be described by means of a single universal equation for all samples at all cluster sizes.

Geometrical structure of disordered sphere packings.

The three-dimensional structure of large packings of monosized spheres with volume fractions ranging between 0.58 and 0.64 has been studied with x-ray computed tomography. We search for signatures of organization, classifying local arrangements and exploring the effects of local geometrical constrains on the global packing. This study is the largest and the most accurate empirical analysis of disordered packings at the grain-scale to date, mapping over 380,000 sphere coordinates with precision within 0.1% of the sphere diameters. We discuss topological and geometrical methods to characterize and classify these systems emphasizing the implications that local geometry can have on the mechanisms of formation of these amorphous structures. Some of the main results are (1) the observation that the average number of contacts increases with the volume fraction; (2) the discovery that these systems have a very compact contact network; (3) the finding that disordered packing can be locally more efficient than crystalline packings; (4) the observation that the peaks of the radial distribution function follow power law divergences; (5) the discovery that geometrical frustration plays no role in the formation of such amorphous packings.

A tool for filtering information in complex systems.

We introduce a technique to filter out complex data sets by extracting a subgraph of representative links. Such a filtering can be tuned up to any desired level by controlling the genus of the resulting graph. We show that this technique is especially suitable for correlation-based graphs, giving filtered graphs that preserve the hierarchical organization of the minimum spanning tree but containing a larger amount of information in their internal structure. In particular in the case of planar filtered graphs (genus equal to 0), triangular loops and four-element cliques are formed. The application of this filtering procedure to 100 stocks in the U.S. equity markets shows that such loops and cliques have important and significant relationships with the market structure and properties.