Scaling power laws in the Sao Paulo Stock Exchange

The scaling of the probability distribution of the Sao Paulo Stock Exchange index is shown to be described by a Levy stable stochastic process for the modal region of the distribution. Data refer to daily records for the 30-year period 1968-1998. The truncated Levy process is characterized by a scaling index of 1.66. Scaling power laws are also shown to be present in the mean and standard deviation of the series as the time horizon is increased. A power law is also found for the autocorrelation time of the natural logs of the index series. The deviations from the line that best fits the natural logs of the series are also found to be short range autocorrelated and to follow an exponential decay.complex systems

The Chinese Chaos Game

The yuan-dollar returns prior to the 2005 revaluation show a Sierpinski triangle in an iterated function system clumpiness test. Yet the fractal vanishes after the revaluation. The Sierpinski commonly emerges in the chaos game, where randomness coexists with deterministic rules [2, 3]. Here it is explained by the yuan’s pegs to the US dollar, which made more than half of the data points close to zero. Extra data from the Brazilian and Argentine experiences do confirm that the fractal emerges whenever exchange rate pegs are kept for too long.

Characteristic function approach to the sum of stochastic variables

This paper puts forward a technique based on the characteristic function to tackle the problem of the sum of stochastic variables. We consider independent processes whose reduced variables are identically distributed, including those that violate the conditions for the central limit theorem to hold. We also consider processes that are correlated and analyze the role of nonlinear autocorrelations in their convergence to a Gaussian. We demonstrate that nonidentity in independent processes is related to autocorrelations in nonindependent processes. We exemplify our approach with data from foreign exchange rates.econophysics; central limit theorem; characteristic function; reduced variables; autocorrelation

Hurst exponents, power laws, and efficiency in the Brazilian foreign exchange market

We find evidence of weak informational efficiency in the Brazilian daily foreign exchange market using Hurst exponents (Hurst 1951, 1955, Feder 1988), which offer an alternative (from statistical physics) to traditional econometric gauges. We show that a trend toward efficiency has been reverted since the crisis of 1999. We also find power laws (Mantegna and Stanley 2000) in means, volatilities, the Hurst exponents, autocorrelation times, and complexity indices of returns for varying time lags.econophysics

The Levy sections theorem revisited

This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end our extension of the theorem provides an approach that is simpler than the more common explicit modeling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analyzing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets.Econophysics; Levy sections