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Assessing time series predictability by extending wavelet energy-based entropy and divergence measures using the Sharma–Mittal framework

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  • Mazzoccoli, Alessandro

Abstract

In this article, we introduce and analyze an extension of existing wavelet energy-based measures for assessing the predictability of a time series: the Sharma–Mittal wavelet energy entropy measure (WSEEM) and the Sharma–Mittal wavelet energy divergence measure (WSEDM). Unlike classical entropy-based measures, such as Shannon’s, which do not have adjustable parameters, and extensions such as those of Rényi and Tsallis, which incorporate a single parameter to modulate the emphasis on high- or low-frequency components, the Sharma–Mittal measure stands out for its greater flexibility. It incorporates two parameters: the first, similar to those of Rényi and Tsallis entropies, controls the focus on different frequency ranges, while the second governs the degree of additivity of entropy for independent systems, i.e., it determines how energy contributions are aggregated.

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  • Mazzoccoli, Alessandro, 2025. "Assessing time series predictability by extending wavelet energy-based entropy and divergence measures using the Sharma–Mittal framework," Chaos, Solitons & Fractals, Elsevier, vol. 201(P3).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p3:s0960077925013645
    DOI: 10.1016/j.chaos.2025.117351
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    References listed on IDEAS

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    1. Mastroeni, Loretta & Mazzoccoli, Alessandro & Vellucci, Pierluigi, 2024. "Studying the impact of fluctuations, spikes and rare events in time series through a wavelet entropy predictability measure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 641(C).
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    3. Masoudi, Oday & Mazzoccoli, Alessandro & Vellucci, Pierluigi, 2025. "Exploring cryptocurrency price dynamics and predictability with ordinal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 674(C).
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    11. Doroshenko, Lyubov & De Crescenzo, Ivan & Mastroeni, Loretta & Mazzoccoli, Alessandro, 2025. "Geopolitical risks, critical materials and energy transition: Insights from wavelet analysis," Resources Policy, Elsevier, vol. 108(C).
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    13. Mastroeni, Loretta & Mazzoccoli, Alessandro, 2024. "Quantifying predictive knowledge: Wavelet energy α-divergence measure for time series uncertainty reduction," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    14. Mastroeni, Loretta & Mazzoccoli, Alessandro & Vellucci, Pierluigi, 2024. "Wavelet entropy and complexity–entropy curves approach for energy commodity price predictability amid the transition to alternative energy sources," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
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    18. Loretta Mastroeni & Alessandro Mazzoccoli & Greta Quaresima & Pierluigi Vellucci, 2021. "Wavelet analysis and energy-based measures for oil-food price relationship as a footprint of financialisation effect," Papers 2104.11891, arXiv.org, revised Mar 2022.
    19. Zunino, Luciano & Tabak, Benjamin M. & Serinaldi, Francesco & Zanin, Massimiliano & Pérez, Darío G. & Rosso, Osvaldo A., 2011. "Commodity predictability analysis with a permutation information theory approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(5), pages 876-890.
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