The near-extreme density of intraday log-returns

The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments. Furthermore, the convergence to the limit distributions can be slow, requiring a huge amount of records to obtain significant statistics, and thus limiting its practical applications. Focussing, instead, on the closely related density of "near-extremes" -- the distance between a record and the maximal value -- can render the statistical methods to be more suitable in the practical applications and/or validations of models. We apply this recently proposed method in the empirical validation of an adapted financial market model of the intraday market fluctuations

Fractional calculus and continuous-time finance II: the waiting-time distribution

We complement the theory of tick-by-tick dynamics of financial markets based on a Continuous-Time Random Walk (CTRW) model recently proposed by Scalas et al., and we point out its consistency with the behaviour observed in the waiting-time distribution for BUND future prices traded at LIFFE, London.Comment: Revised version, 17 pages, 4 figures. Physica A, Vol. 287, No 3-4, 468--481 (2000). Proceedings of the International Workshop on "Economic Dynamics from the Physics Point of View", Bad-Honnef (Germany), 27-30 March 200

Generalization of multifractal theory within quantum calculus

On the basis of the deformed series in quantum calculus, we generalize the partition function and the mass exponent of a multifractal, as well as the average of a random variable distributed over self-similar set. For the partition function, such expansion is shown to be determined by binomial-type combinations of the Tsallis entropies related to manifold deformations, while the mass exponent expansion generalizes the known relation $\tau_q=D_q(q-1)$. We find equation for set of averages related to ordinary, escort, and generalized probabilities in terms of the deformed expansion as well. Multifractals related to the Cantor binomial set, exchange currency series, and porous surface condensates are considered as examples. Keywords:Multifractal set; Deformation; Power series.Comment: 12 pages, 4 figures, accepted by EP

Non-parametric Estimation of Stochastic Differential Equations with Sparse Gaussian Processes

The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a non-parametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudo-samples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behaviour of complex systems

Organization of networks with tagged nodes and biased links: a priori distinct communities. The case of Intelligent Design Proponents and Darwinian Evolution Defenders

Among topics of opinion formation it is of interest to observe the characteristics of networks with a priori distinct communities. As an illustration, we report on the citation network(s) unfolded in the recent decades through web available works belonging to selected members of the Neocreationist and Intelligent Design Proponents (IDP) and the Darwinian Evolution Defenders (DED) communities. An adjacency matrix of tagged nodes is first constructed; it is not symmetric. A generalization of considerations pertaining to the case of networks with biased links, directed or undirected, is thus presented. The main characteristic coefficients describing the structure of such partially directed networks with tagged nodes are outlined. The structural features are discussed searching for statistical aspects, equivalence or not of subnetworks through the degree distributions, each network assortativity, the global and local clustering coefficients and the Average Overlap Indices. The various closed and open triangles made from nodes, moreover distinguishing the community, are especially listed to calculate the clustering characteristics. The distribution of elements in the rectangular submatrices are specially examined since they represent inter-community connexions. The emphasis being on distinguishing the number of vertices belonging to a given community. Using such informations one can distinguish between opinion leaders, followers and main rivals and briefly interpret their relationships through psychological-like conditions intrinsic to behavior rules in either community. Considerations on other controversy cases with similar social constraints are outlined, as well as suggestions on further, more general, work deduced from our observations on such networks.Comment: 40 pages, 61 references, 7 Tables, 11 Figures, 2 Appendices (giving the adjacency matrices

A Multi Agent Model for the Limit Order Book Dynamics

In the present work we introduce a novel multi-agent model with the aim to reproduce the dynamics of a double auction market at microscopic time scale through a faithful simulation of the matching mechanics in the limit order book. The agents follow a noise decision making process where their actions are related to a stochastic variable, "the market sentiment", which we define as a mixture of public and private information. The model, despite making just few basic assumptions over the trading strategies of the agents, is able to reproduce several empirical features of the high-frequency dynamics of the market microstructure not only related to the price movements but also to the deposition of the orders in the book.Comment: 20 pages, 11 figures, in press European Physical Journal B (EPJB