Noise versus chaos in a causal Fisher-Shannon plane

We revisit the Fisher-Shannon representation plane ${\mathcal H} \times {\mathcal F}$, evaluated using the Bandt and Pompe recipe to assign a probability distribution to a time series. Several stochastic dynamical (noises with $f^{-k}$, $k \geq 0$, power spectrum) and chaotic processes (27 chaotic maps) are analyzed so as to illustrate the approach. Our main achievement is uncovering the informational properties of the planar location.Comment: 6 pages, 1 figure. arXiv admin note: text overlap with arXiv:1401.213

Efficiency characterization of a large neuronal network: a causal information approach

When inhibitory neurons constitute about 40% of neurons they could have an important antinociceptive role, as they would easily regulate the level of activity of other neurons. We consider a simple network of cortical spiking neurons with axonal conduction delays and spike timing dependent plasticity, representative of a cortical column or hypercolumn with large proportion of inhibitory neurons. Each neuron fires following a Hodgkin-Huxley like dynamics and it is interconnected randomly to other neurons. The network dynamics is investigated estimating Bandt and Pompe probability distribution function associated to the interspike intervals and taking different degrees of inter-connectivity across neurons. More specifically we take into account the fine temporal ``structures'' of the complex neuronal signals not just by using the probability distributions associated to the inter spike intervals, but instead considering much more subtle measures accounting for their causal information: the Shannon permutation entropy, Fisher permutation information and permutation statistical complexity. This allows us to investigate how the information of the system might saturate to a finite value as the degree of inter-connectivity across neurons grows, inferring the emergent dynamical properties of the system.Comment: 26 pages, 3 Figures; Physica A, in pres

Classification and Verification of Online Handwritten Signatures with Time Causal Information Theory Quantifiers

We present a new approach for online handwritten signature classification and verification based on descriptors stemming from Information Theory. The proposal uses the Shannon Entropy, the Statistical Complexity, and the Fisher Information evaluated over the Bandt and Pompe symbolization of the horizontal and vertical coordinates of signatures. These six features are easy and fast to compute, and they are the input to an One-Class Support Vector Machine classifier. The results produced surpass state-of-the-art techniques that employ higher-dimensional feature spaces which often require specialized software and hardware. We assess the consistency of our proposal with respect to the size of the training sample, and we also use it to classify the signatures into meaningful groups.Comment: Submitted to PLOS On

Libor at crossroads: stochastic switching detection using information theory quantifiers

This paper studies the 28 time series of Libor rates, classified in seven maturities and four currencies), during the last 14 years. The analysis was performed using a novel technique in financial economics: the Complexity-Entropy Causality Plane. This planar representation allows the discrimination of different stochastic and chaotic regimes. Using a temporal analysis based on moving windows, this paper unveals an abnormal movement of Libor time series arround the period of the 2007 financial crisis. This alteration in the stochastic dynamics of Libor is contemporary of what press called "Libor scandal", i.e. the manipulation of interest rates carried out by several prime banks. We argue that our methodology is suitable as a market watch mechanism, as it makes visible the temporal redution in informational efficiency of the market.Comment: 17 pages, 9 figures. arXiv admin note: text overlap with arXiv:1508.04748, arXiv:1509.0021

The (in)visible hand in the Libor market: an Information Theory approach

This paper analyzes several interest rates time series from the United Kingdom during the period 1999 to 2014. The analysis is carried out using a pioneering statistical tool in the financial literature: the complexity-entropy causality plane. This representation is able to classify different stochastic and chaotic regimes in time series. We use sliding temporal windows to assess changes in the intrinsic stochastic dynamics of the time series. Anomalous behavior in the Libor is detected, especially around the time of the last financial crisis, that could be consistent with data manipulation.Comment: PACS 89.65.Gh Econophysics; 74.40.De noise and chao

A permutation Information Theory tour through different interest rate maturities: the Libor case

This paper analyzes Libor interest rates for seven different maturities and referred to operations in British Pounds, Euro, Swiss Francs and Japanese Yen, during the period years 2001 to 2015. The analysis is performed by means of two quantifiers derived from Information Theory: the permutation Shannon entropy and the permutation Fisher information measure. An anomalous behavior in the Libor is detected in all currencies except Euro during the years 2006--2012. The stochastic switch is more severe in 1, 2 and 3 months maturities. Given the special mechanism of Libor setting, we conjecture that the behavior could have been produced by the manipulation that was uncovered by financial authorities. We argue that our methodology is pertinent as a market overseeing instrument.Comment: arXiv admin note: text overlap with arXiv:1304.039

Characterizing the Hyperchaotic Dynamics of a Semiconductor Laser Subject to Optical Feedback Via Permutation Entropy

The time evolution of the output of a semiconductor laser subject to delayed optical feedback can exhibit highdimensional chaotic fluctuations. In this contribution, our aim is to quantify the degree of unpredictability of this hyperchaotic time evolution. To that end, we estimate permutation entropy, a novel information-theory-derived quantifier particularly robust in a noisy environment. The permutation entropy is defined as a functional of a symbolic probability distribution, evaluated using the Bandt-Pompe recipe to assign a probability distribution function to the time series generated by the chaotic system. This measure quantifies the diversity of orderings present in the associated time series. In order to evaluate the performance of this novel quantifier, we compare with the results obtained by using a more standard chaos quantifier, namely the KolmogorovSinai entropy. Here, we present numerical results showing that the permutation entropy, evaluated at specific time-scales involved in the chaotic regime of the semiconductor laser subject to optical feedback, give valuable information about the degree of unpredictability of the chaotic laser dynamics. The influence of additive observational noise on the proposed tool is also investigated.L.Z. and O.A.R. were supported by Consejo Nacional de Investigaciones Cient´ıficas y T´ecnicas (CONICET), Argentina. O.A.R. is PVE fellowship, CAPES, Brazil. Part of this work was funded by MEC (Spain), MICINN (Spain) and FEDER under Projects TEC2009-14101 (DeCoDicA) and FIS2007-60327 (FISICOS), and by the EC Project PHOCUS Grant 240763.Peer reviewe