Long-Range Correlations and Characterization of Financial and Volcanic Time Series

Abstract

In this study, we use the Diffusion Entropy Analysis (DEA) to analyze and detect the scaling properties of time series from both emerging and well established markets as well as volcanic eruptions recorded by a seismic station, both financial and volcanic time series data have high frequencies. The objective is to determine whether they follow a Gaussian or Lévy distribution, as well as establish the existence of long-range correlations in these time series. The results obtained from the DEA technique are compared with the Hurst R/S analysis and Detrended Fluctuation Analysis (DFA) methodologies. We conclude that these methodologies are effective in classifying the high frequency financial indices and volcanic eruption data—the financial time series can be characterized by a Lévy walk while the volcanic time series is characterized by a Lévy flight.

A New EEMD‐Effective Transfer Entropy‐Based Methodology for Exchange Rate Market Information Transmission in Southern Africa Development Community

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Why quadratic log-log dependence is ubiquitous and what next

“…In other words, we have a quadratic log-log dependence, of which the linear log-log dependence (3) is a particular case corresponding to b 1 = 0. Such dependencies is really ubiquitous: e.g., an empirical analysis provided in [2] have shown that many real-life dependencies, ranging from economic to volcanic data, follow these formulas. This naturally leads to the following questions.…”

Relationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set

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“…Empirical evidence has shown that the DFA has the tendency of overestimating the scaling exponent [2,22]. We have not come accross any literature at the moment that describes a definite approach in the segment division step of the DFA algorithm.…”