长期记忆与分形维度：阿尔坎塔拉案例研究
The Long-Range Memory and the Fractal Dimension: a Case Study for Alcântara
AI总结：
本文通过快速傅里叶变换、自相关函数和Hurst系数计算分析南半球振荡指数的时间序列行为，揭示其长期记忆特性及分形维度，探讨其对巴西东北部气候的影响。
摘要：
本研究旨在通过快速傅里叶变换、计算自相关函数和Hurst系数来分析南半球振荡指数的时间序列行为。Hurst指数的计算方法使用不同的滞后，这些滞后是通过南半球振荡指数的时间序列计算得出的。通过计算Hurst指数可以表征时间序列的持久行为，以获取更多行为信息，如持久性和长期记忆的存在。结果表明，气候在长期记忆方面的持续性，有助于理解全球尺度上的复杂动态行为及其对巴西东北部的影响，特别是对阿尔坎塔拉发射中心的影响。R包tseriesChaos被用于分析南半球振荡指数的时间序列，估计最大李雅普诺夫指数，表明时间序列中存在混沌行为。在萨翁·路易斯机场的表面风数据与南半球振荡指数之间进行了重新抽样技术的置换检验。置换检验结果表明，萨翁·路易斯机场的月平均风速时间序列与南半球振荡指数的变异性在5%的置信水平上具有统计学显著性。结果还表明，使用自回归模型来表示平均气象变量在行为分析中的可能性，以及气候趋势，特别是厄尔尼诺-南方涛动对阿尔坎塔拉发射中心风速的影响的可能性。
英文摘要：
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, such 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 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 \texttt{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 significant at the 5\% confidence level. The results also indicate the possibility of using autoregressive models to represent average meteorological variables in behavioral analysis, as well as trends in the climate, more specifically a possible climatic influence of El Niño--Southern Oscillation on wind strength in the Alcântara Launch Center.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
