Raul Matsushita

Exponentially damped Lévy flights

Since real processes seem to departure from standard Levy distributions, modifications to the latter have been suggested in literature. These include (abruptly) truncated (Phys. Rev. Lett. 73 (1994) 2946), smoothly truncated (Phys. Rev. E 52 (1995) 1197; Phys. Lett. A 266 (2000) 282) and gradually truncated Levy flights (Physica A 268 (1999) 231; Physica A 275 (2000) 531). We put forward what we call an exponentially damped Levy flight which encompasses the previous cases. In the presence of increasing and positive feedbacks, our distribution is assumed to deviate from the Levy in both a smooth and gradual fashion. We estimate the truncation parameters by nonlinear least squares to optimally fit the distribution tails. That is a novel approach for estimating parameters α and γ of the Levy. The method is illustrated with daily data on exchange rates for 15 countries against the US dollar. Our results show that the exponentially damped Levy flight fits the data well when increasing and positive deviations are present.

Autocorrelation as a source of truncated Lévy flights in foreign exchange rates

We suggest that the ultraslow speed of convergence associated with truncated Levy flights (Phys. Rev. Lett. 73 (1994) 2946) may well be explained by autocorrelations in data. We show how a particular type of autocorrelation generates power laws consistent with a truncated Levy flight. Stock exchanges have been suggested to be modeled by a truncated Levy flight (Nature 376 (1995) 46; Physica A 297 (2001) 509; Econom. Bull. 7 (2002) 1). Here foreign exchange rate data are taken instead. Scaling power laws in the “probability of return to the origin” are shown to emerge for most currencies. A novel approach to measure how distant a process is from a Gaussian regime is presented.

Algorithmic complexity theory and the relative efficiency of financial markets

Financial economists usually assess market efficiency in absolute terms. This is to be viewed as a shortcoming. One way of dealing with the relative efficiency of markets is to resort to the efficiency interpretation provided by algorithmic complexity theory. We employ such an approach in order to rank 36 stock exchanges and 20 US dollar exchange rates in terms of their relative efficiency.

Sistemas complexos, criticalidade e leis de potência

Neste texto fazemos um apanhado inicial e geral das principais id¥eias relacionadas a teoria dos sistemas complexos.

On the Origins of Truncated Levy Flights

Abstract We show that truncated Levy flights appear due to the presence of particular features of autocorrelation in data. We present and analyze ‘physical’ reasons sufficient to ensure the scaling power laws and sluggish convergence associated with truncated Levy flights. Our approach is exemplified with currency data for the British pound and Chinese yuan against the US dollar. We further compare these examples with a simulated Lorentzian distribution.

Efficiency of financial markets and algorithmic complexity

In this work we are interested in the concept of market efficiency and its relationship with the algorithmic complexity theory. We employ a methodology based on the Lempel-Ziv index to analyze the relative efficiency of high-frequency data coming from the Brazilian stock market.

Debt of high-income consumers may reflect leverage rather than poor cognitive reflection

A recent population-wide study for Germany, where credit lines on current accounts are available to 80 percent of the population, finds that overdraft debt is more likely for people who give intuitive but incorrect answers on a cognitive reflection test. This suggests those consumers in debt have poorer cognitive reflection and, thus, lack of self control. The Germany study finds that “surprisingly, the level of income does not play a central role.” Here we discriminate the consumers in terms of their income by considering two experiments. In the first (pilot) experiment we do not discriminate consumers in terms of income and, as result, replicate the Germany study. In a follow-up experiment, which assembles a high-quality sample of high-income consumers, we find debt can no longer be explained by poor cognitive reflection. Apparently, high-income consumers treat debt as mere leverage, as companies do.

Lotka’s law for the Brazilian scientific output published in journals

Lotka’s law is a power law for the frequency of scholarly publications. We show that Lotka’s law cannot be dismissed after considering a massive sample of the number of publications of Brazilian researchers in journals listed on the SCImago Journal Rank and the Journal Citation Reports. For the SCImago Journal Rank, we found a power law with the Pareto exponent of 0.4 beyond the threshold of 50 papers. This means computing the ‘average number of publications’ of either a researcher or a discipline is of no practical significance.

The Touchard distribution

ABSTRACT We present a novel model, which is a two-parameter extension of the Poisson distribution. Its normalizing constant is related to the Touchard polynomials, hence the name of this model. It is a flexible distribution that can account for both under- or overdispersion and concentration of zeros that are frequently found in non-Poisson count data. In contrast to some other generalizations, the Hessian matrix for maximum likelihood estimation of the Touchard parameters has a simple form. We exemplify with three data sets, showing that our suggested model is a competitive candidate for fitting non-Poisson counts.