Non-Poisson dichotomous noise: higher-order correlation functions and aging

We study a two-state symmetric noise, with a given waiting time distribution $\psi (\tau)$, and focus our attention on the connection between the four-time and the two-time correlation functions. The transition of $\psi (\tau)$ from the exponential to the non-exponential condition yields the breakdown of the usual factorization condition of high-order correlation functions, as well as the birth of aging effects. We discuss the subtle connections between these two properties, and establish the condition that the Liouville-like approach has to satisfy in order to produce a correct description of the resulting diffusion process

Non-Poisson dichotomous noise: higher-order correlation functions and aging

We study a two-state symmetric noise, with a given waiting time distribution $\psi (\tau)$, and focus our attention on the connection between the four-time and the two-time correlation functions. The transition of $\psi (\tau)$ from the exponential to the non-exponential condition yields the breakdown of the usual factorization condition of high-order correlation functions, as well as the birth of aging effects. We discuss the subtle connections between these two properties, and establish the condition that the Liouville-like approach has to satisfy in order to produce a correct description of the resulting diffusion process

Facing Non-Stationary Conditions with a New Indicator of Entropy Increase: The Cassandra Algorithm

We address the problem of detecting non-stationary effects in time series (in particular fractal time series) by means of the Diffusion Entropy Method (DEM). This means that the experimental sequence under study, of size $N$, is explored with a window of size $L << N$. The DEM makes a wise use of the statistical information available and, consequently, in spite of the modest size of the window used, does succeed in revealing local statistical properties, and it shows how they change upon moving the windows along the experimental sequence. The method is expected to work also to predict catastrophic events before their occurrence.Comment: FRACTAL 2002 (Spain

Climate change assessment for Mediterranean agricultural areas by statistical downscaling

In this paper we produce projections of seasonal precipitation for four Mediterranean areas: Apulia region (Italy), Ebro river basin (Spain), Po valley (Italy) and Antalya province (Turkey). We performed the statistical downscaling using Canonical Correlation Analysis (CCA) in two versions: in one case Principal Component Analysis (PCA) filter is applied only to predictor and in the other to both predictor and predictand. After performing a validation test, CCA after PCA filter on both predictor and predictand has been chosen. Sea level pressure (SLP) is used as predictor. Downscaling has been carried out for the scenarios A2 and B2 on the basis of three GCM's: the CCCma-GCM2, the Csiro-MK2 and HadCM3. Three consecutive 30-year periods have been considered. For Summer precipitation in Apulia region we also use the 500 hPa temperature (T500) as predictor, obtaining comparable results. Results show different climate change signals in the four areas and confirm the need of an analysis that is capable of resolving internal differences within the Mediterranean region. The most robust signal is the reduction of Summer precipitation in the Ebro river basin. Other significative results are the increase of precipitation over Apulia in Summer, the reduction over the Po-valley in Spring and Autumn and the increase over the Antalya province in Summer and Autumn

Compression and diffusion: a joint approach to detect complexity

The adoption of the Kolmogorov-Sinai (KS) entropy is becoming a popular research tool among physicists, especially when applied to a dynamical system fitting the conditions of validity of the Pesin theorem. The study of time series that are a manifestation of system dynamics whose rules are either unknown or too complex for a mathematical treatment, is still a challenge since the KS entropy is not computable, in general, in that case. Here we present a plan of action based on the joint action of two procedures, both related to the KS entropy, but compatible with computer implementation through fast and efficient programs. The former procedure, called Compression Algorithm Sensitive To Regularity (CASToRe), establishes the amount of order by the numerical evaluation of algorithmic compressibility. The latter, called Complex Analysis of Sequences via Scaling AND Randomness Assessment (CASSANDRA), establishes the complexity degree through the numerical evaluation of the strength of an anomalous effect. This is the departure, of the diffusion process generated by the observed fluctuations, from ordinary Brownian motion. The CASSANDRA algorithm shares with CASToRe a connection with the Kolmogorov complexity. This makes both algorithms especially suitable to study the transition from dynamics to thermodynamics, and the case of non-stationary time series as well. The benefit of the joint action of these two methods is proven by the analysis of artificial sequences with the same main properties as the real time series to which the joint use of these two methods will be applied in future research work.Comment: 27 pages, 9 figure

Effects of vertical shear in modelling horizontal oceanic dispersion

Abstract. The effect of vertical shear on the horizontal dispersion properties of passive tracer particles on the continental shelf of the South Mediterranean is investigated by means of observation and model data. In situ current measurements reveal that vertical gradients of horizontal velocities in the upper mixing layer decorrelate quite fast ( ∼  1 day), whereas an eddy-permitting ocean model, such as the Mediterranean Forecasting System, tends to overestimate such decorrelation time because of finite resolution effects. Horizontal dispersion, simulated by the Mediterranean sea Forecasting System, is mostly affected by: (1) unresolved scale motions, and mesoscale motions that are largely smoothed out at scales close to the grid spacing; (2) poorly resolved time variability in the profiles of the horizontal velocities in the upper layer. For the case study we have analysed, we show that a suitable use of deterministic kinematic parametrizations is helpful to implement realistic statistical features of tracer dispersion in two and three dimensions. The approach here suggested provides a functional tool to control the horizontal spreading of small organisms or substance concentrations, and is thus relevant for marine biology, pollutant dispersion as well as oil spill applications

Activity autocorrelation in financial markets. A comparative study between several models

We study the activity, i.e., the number of transactions per unit time, of financial markets. Using the diffusion entropy technique we show that the autocorrelation of the activity is caused by the presence of peaks whose time distances are distributed following an asymptotic power law which ultimately recovers the Poissonian behavior. We discuss these results in comparison with ARCH models, stochastic volatility models and multi-agent models showing that ARCH and stochastic volatility models better describe the observed experimental evidences.Comment: 15 pages, 4 figure

Correlation function and generalized master equation of arbitrary age

We study a two-state statistical process with a non-Poisson distribution of sojourn times. In accordance with earlier work, we find that this process is characterized by aging and we study three different ways to define the correlation function of arbitrary age of the corresponding dichotomous fluctuation based respectively on the Generalized Master Equation formalism, on a Liouville-like approach and on a trajectory perspective.Comment: 11 pages, 1figur

Entropy of the Nordic electricity market: anomalous scaling, spikes, and mean-reversion

The electricity market is a very peculiar market due to the large variety of phenomena that can affect the spot price. However, this market still shows many typical features of other speculative (commodity) markets like, for instance, data clustering and mean reversion. We apply the diffusion entropy analysis (DEA) to the Nordic spot electricity market (Nord Pool). We study the waiting time statistics between consecutive spot price spikes and find it to show anomalous scaling characterized by a decaying power-law. The exponent observed in data follows a quite robust relationship with the one implied by the DEA analysis. We also in terms of the DEA revisit topics like clustering, mean-reversion and periodicities. We finally propose a GARCH inspired model but for the price itself. Models in the context of stochastic volatility processes appear under this scope to have a feasible description.Comment: 16 pages, 7 figure