IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v202y2026ip2s0960077925015668.html

Beyond volatility: Using differential entropy to detect financial market regimes

Author

Listed:
  • Matsushita, Raul
  • Nobre, Iuri
  • Da Silva, Sergio

Abstract

Financial markets alternate between calm and turbulent phases, but volatility alone often fails to reveal structural changes in uncertainty. This study develops a differential entropy approach that detects market regimes through shifts in distributional complexity rather than moment-based variability. The method employs a data-adaptive heavy-tailed kernel, yielding a consistent and scale-invariant entropy estimator that remains valid under dependent dynamics. Monte Carlo experiments confirm its robustness and sensitivity to tail transitions. When applied to major stock indices from 1998 to 2025, the entropy-based indicator identifies heavy-tailed regimes that align with well-known episodes of financial distress, including the Dot-com Bubble, Global Financial Crisis, COVID-19 shock, and the 2025 tariff crisis, while Gaussian regimes characterize periods of market efficiency. The results demonstrate that variance and entropy may diverge during crises, indicating that entropy captures forms of uncertainty invisible to volatility. Overall, the framework offers a nonparametric and information-theoretic tool for regime detection and systemic risk assessment in complex financial systems.

Suggested Citation

  • Matsushita, Raul & Nobre, Iuri & Da Silva, Sergio, 2026. "Beyond volatility: Using differential entropy to detect financial market regimes," Chaos, Solitons & Fractals, Elsevier, vol. 202(P2).
    • Handle: RePEc:eee:chsofr:v:202:y:2026:i:p2:s0960077925015668
    DOI: 10.1016/j.chaos.2025.117553
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925015668
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.117553?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Freire, Gustavo, 2021. "Tail risk and investors’ concerns: Evidence from Brazil," The North American Journal of Economics and Finance, Elsevier, vol. 58(C).
    2. Bijsterbosch, Martin & Guérin, Pierre, 2013. "Characterizing very high uncertainty episodes," Economics Letters, Elsevier, vol. 121(2), pages 239-243.
    3. Luiz G. A. Alves & Higor Y. D. Sigaki & Matjaz Perc & Haroldo V. Ribeiro, 2020. "Collective dynamics of stock market efficiency," Papers 2011.14809, arXiv.org.
    4. Eom, Cheoljun & Kaizoji, Taisei & Scalas, Enrico, 2019. "Fat tails in financial return distributions revisited: Evidence from the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    5. Kaizoji, Taisei & Miyano, Michiko, 2016. "Why does the power law for stock price hold?," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 19-23.
    6. Valeriy Zakamulin, 2023. "Revisiting the duration dependence in the US stock market cycles," Applied Economics, Taylor & Francis Journals, vol. 55(4), pages 357-368, January.
    7. Mantegna, Rosario N. & Stanley, H.Eugene, 1998. "Modeling of financial data: Comparison of the truncated Lévy flight and the ARCH(1) and GARCH(1,1) processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 254(1), pages 77-84.
    8. Peter Hall & Sally Morton, 1993. "On the estimation of entropy," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(1), pages 69-88, March.
    9. Eom, Cheoljun & Kaizoji, Taisei & Livan, Giacomo & Scalas, Enrico, 2021. "Limitations of portfolio diversification through fat tails of the return Distributions: Some empirical evidence," The North American Journal of Economics and Finance, Elsevier, vol. 56(C).
    10. Tran, Quang Van & Kukal, Jaromir, 2022. "A novel heavy tail distribution of logarithmic returns of cryptocurrencies," Finance Research Letters, Elsevier, vol. 47(PA).
    11. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
    12. Eom, Cheoljun & Park, Jong Won, 2020. "Effects of the fat-tail distribution on the relationship between prospect theory value and expected return," The North American Journal of Economics and Finance, Elsevier, vol. 51(C).
    13. Chen, Yan & Liu, Yakun, 2024. "Idiosyncratic asymmetry in stock returns: An entropy measure," Finance Research Letters, Elsevier, vol. 64(C).
    14. Matsushita, Raul & Brandão, Helena & Nobre, Iuri & Da Silva, Sergio, 2024. "Differential entropy estimation with a Paretian kernel: Tail heaviness and smoothing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 646(C).
    15. Ardakani, Omid M., 2023. "Capturing information in extreme events," Economics Letters, Elsevier, vol. 231(C).
    16. Fernandez-Mejia, Julian, 2024. "Extremely stablecoins," Finance Research Letters, Elsevier, vol. 63(C).
    17. Higor Y. D. Sigaki & Matjaz Perc & Haroldo V. Ribeiro, 2019. "Clustering patterns in efficiency and the coming-of-age of the cryptocurrency market," Papers 1901.04967, arXiv.org.
    18. Dorea, Chang C.Y. & Guevara Otiniano, Cira E. & Matsushita, Raul & Rathie, Pushpa N., 2007. "Levy flight approximations for scaled transformations of random walks," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6343-6354, August.
    19. Van Tran, Quang & Kukal, Jaromir, 2024. "Renyi entropy based design of heavy tailed distribution for return of financial assets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    20. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fernandes, Leonardo H.S. & Figueirôa, José R.A. & Martins, Caleb M.F. & Martins, Adriel M.F., 2025. "The battle of informational efficiency: Cryptocurrencies vs. classical assets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 664(C).
    2. Marcin Wk{a}torek & Jaros{l}aw Kwapie'n & Stanis{l}aw Dro.zd.z, 2021. "Financial Return Distributions: Past, Present, and COVID-19," Papers 2107.06659, arXiv.org.
    3. Eom, Cheoljun & Eom, Yunsung & Park, Jong Won, 2023. "Left-tail momentum and tail properties of return distributions: A case of Korea," International Review of Financial Analysis, Elsevier, vol. 87(C).
    4. Athanasia Gavala & Nikolay Gospodinov & Deming Jiang, 2006. "Forecasting volatility," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(6), pages 381-400.
    5. Chia-Lin Chang & Tai-Lin Hsieh & Michael McAleer, 2016. "Connecting VIX and Stock Index ETF," Tinbergen Institute Discussion Papers 16-010/III, Tinbergen Institute, revised 23 Jan 2017.
    6. Stentoft, Lars, 2005. "Pricing American options when the underlying asset follows GARCH processes," Journal of Empirical Finance, Elsevier, vol. 12(4), pages 576-611, September.
    7. Nico Knuth & Andreas Nastansky, 2025. "Anwendung von Deep Learning in der Prognose der Volatilität des DAX: Ein Vergleich der Prognosegüte von GARCH und LSTM," Statistische Diskussionsbeiträge 59, Universität Potsdam, Wirtschafts- und Sozialwissenschaftliche Fakultät.
    8. Charles, Amélie, 2010. "The day-of-the-week effects on the volatility: The role of the asymmetry," European Journal of Operational Research, Elsevier, vol. 202(1), pages 143-152, April.
    9. Chao Wang & Richard Gerlach, 2021. "A Bayesian realized threshold measurement GARCH framework for financial tail risk forecasting," Papers 2106.00288, arXiv.org, revised Oct 2022.
    10. E. Ramos-P'erez & P. J. Alonso-Gonz'alez & J. J. N'u~nez-Vel'azquez, 2020. "Forecasting volatility with a stacked model based on a hybridized Artificial Neural Network," Papers 2006.16383, arXiv.org, revised Aug 2020.
    11. Blagica Novkovska & Gordana Serafimovic, 2018. "Recognizing The Vulnerability Of Generation Z To Economic And Social Risks," UTMS Journal of Economics, University of Tourism and Management, Skopje, Macedonia, vol. 9(1), pages 29-37.
    12. CHIA-LIN CHANG & MICHAEL McALEER & ROENGCHAI TANSUCHAT, 2012. "Modelling Long Memory Volatility In Agricultural Commodity Futures Returns," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 1-27.
    13. Wei Liu & Bruce Morley, 2009. "Volatility Forecasting in the Hang Seng Index using the GARCH Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(1), pages 51-63, March.
    14. Orkun ÇELİK & Deniz ERER & Elif ERER, 2018. "2008 Küresel Krizinin Bireysel Emeklilik Fonları Oynaklığı Üzerindeki Etkisi: Türkiye Örneği," Sosyoekonomi Journal, Sosyoekonomi Society, issue 26(35).
    15. Abdmoulah, Walid, 2010. "Testing the evolving efficiency of Arab stock markets," International Review of Financial Analysis, Elsevier, vol. 19(1), pages 25-34, January.
    16. Mehmet Sahiner, 2022. "Forecasting volatility in Asian financial markets: evidence from recursive and rolling window methods," SN Business & Economics, Springer, vol. 2(10), pages 1-74, October.
    17. Chris Motengwe & Angel Pardo, 2015. "A Study of Seasonality on the Safex Wheat Market," Agrekon, Taylor & Francis Journals, vol. 54(4), pages 45-72, November.
    18. Gavriilidis, Konstantinos & Kambouroudis, Dimos S. & Tsakou, Katerina & Tsouknidis, Dimitris A., 2018. "Volatility forecasting across tanker freight rates: The role of oil price shocks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 376-391.
    19. Koopman, Siem Jan & Jungbacker, Borus & Hol, Eugenie, 2005. "Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 445-475, June.
    20. Lars Stentoft, 2008. "Option Pricing using Realized Volatility," CREATES Research Papers 2008-13, Department of Economics and Business Economics, Aarhus University.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:202:y:2026:i:p2:s0960077925015668. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.