The Long-Range Memory and the Fractal Dimension: a Case Study for Alcântara

Cleber Souza Corrêa, Daniel Andrade Schuch, Antonio Paulo De Queiroz, Gilberto Fernando Fisch, Felipe do Nascimento Corrêa, Mariane Mendes Coutinho


This study aimed to analyze the time series behavior of the Southern Oscillation Index through techniques using Fast Fourier Transform, computing the autocorrelation function, and the calculation of the Hurst coefficient. The methodology of Hurst Exponent calculation uses different lags, which are computed in the time series of Southern Oscillation Index. The persistent behavior in the time series can be characterized by calculating the Hurst Exponent, seeking for more behavioral information, as the existence of persistence and/or terms of long-range memory in the series. The results show a persistence of the climate in terms of long-memory Southern Oscillation Index time series, which can help to understand a complex dynamic behavior in climate effects at global-scale level and specifically its influence in northeastern Brazil, in the region of the Alcântara Launch Center. The R package tseriesChaos was used in the analysis of the Southern Oscillation Index time series, estimating the largest Lyapunov exponent, which indicates the existence of chaotic behavior in time series. The resampling technique was used in a permutation test between the surface wind data in the São Luís airport, Maranhão State, and the Southern Oscillation Index. The permutation test results showed that the time series of monthly average wind speed in the São Luís airport is correlated with the variability of Southern Oscillation Index, statistically correlated to the confidence interval at the 5% level. The results showed the possibility of using autoregressive models to represent average variable meteorology in the behavior analysis as well as trends in the climate, more specifically a possible climatic influence of El Niño-Southern Oscillation in wind strength in the Alcântara Launch Center.


Time-series analysis; Hurst exponent; Permutation Test

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