International Journal of Finance & Managerial Accounting

International Journal of Finance & Managerial Accounting

Causal Relationship between Permutation Entropy and Financial Market Crises: A Granger Causality Approach

Articles in Press

Document Type : Original Article

Authors
Masoume Ramezani 1
Fraydoon Rahnamay Roodposhti 2
ghanbar Abbaspour Esfeden 3
1 Department of Industrial Management, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 Department of Accounting and Management, Science and Research Branch, Islamic Azad University, Tehran, Iran
3 Department of Industrial Management, South Tehran Branch, Islamic Azad University, Tehran, Iran
10.22034/ijfma.2026.78676.2292
Abstract
This study examines the causal relationship between permutation entropy (PE) and financial market crises through a Granger causality framework. Time series data from several major global indices are analyzed to assess whether permutation entropy can effectively serve as a predictor of financial instability. The results indicate that permutation entropy significantly Granger-causes crises in selected markets such as the DAX, Nasdaq 100, and Nikkei 225, suggesting its value as an early warning indicator in those regions. However, no significant predictive relationship is observed for indices including the Dow Jones, S&P 500, Shanghai Composite, SZSE Composite, and TSX Composite. These findings highlight regional differences in the predictive power of permutation entropy , likely shaped by market-specific dynamics and regulatory structures. This research underscores the potential applications and inherent limitations of permutation entropy in crisis forecasting and encourages future studies to incorporate additional nonlinear indicators and localized market factors to improve predictive accuracy.
Keywords: Permutation entropy, Financial crises, Granger causality, Time series, Early warning indicator.
Keywords
Permutation entropy
Financial crises
Granger causality
Time series
Early warning indicator
1.      Allen, F., Qian, J., & Qian, M. (2017). China’s financial system and the law. Cornell International Law Journal, 50(2), 225–256.
2.      Alves, L. G. A., Sigaki, H. Y. D., Perc, M., & Ribeiro, H. V. (2020). Collective dynamics of stock market efficiency. Scientific Reports, 10(1),21992.      https://doi.org/10.1038/s41598-020-77912-3
3.      Bandt, C., & Pompe, B. (2002). Permutation entropy: A natural complexity measure for time series. Physical Review Letters, 88(17), 174102. https://doi.org/10.1103/PhysRevLett.88.174102
4.      Basel Committee on Banking Supervision. (2011). Basel III: A global regulatory framework for more resilient banks and banking systems. Bank for International Settlements. https://www.bis.org/publ/bcbs189.htm
5.      Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307–327. https://doi.org/10.1016/0304-4076(86)90063-1
6.      Brownlees, C., & Engle, R. F. (2017). SRISK: A conditional capital shortfall measure of systemic risk. The Review of Financial Studies, 30(1), 48-79. https://doi.org/10.1093/rfs/hhw060
7.      Claessens, S., Kose, M. A., & Terrones, M. E. (2012). How do business and financial cycles interact? Journal of International Economics, 87(1), 178-190. https://doi.org/10.1016/j.jinteco.2011.11.008
8.      Croux, C., & Reusens, P. (2013). Do stock prices contain predictive power for the future economic activity? A Granger causality analysis in the frequency domain. Journal of Macroeconomics, 35, 93-103. https://doi.org/10.1016/j.jmacro.2012.10.003
9.      Danks, D., & Davis, I. (2023). Causal inference in cognitive neuroscience. Wiley Interdisciplinary Reviews: Cognitive Science, 14(5), e1650. https://doi.org/10.1002/wcs.1650
10.  Danylchuk, H. B., & Solovyova, V. V. (2016). Application of permutation entropy for predictive analysis of crisis phenomena in the stock market. Bulletin of Cherkasy Bohdan Khmelnytsky National University: Economic Sciences, (3), 1–12. Retrieved from https://econom-ejournal.cdu.edu.ua/article/view/2235
11.  Durukan, M. B., Özsu, H. H., & Ergun, Z. C. (2017). Financial crisis and herd behavior: Evidence from the Borsa Istanbul. In Handbook of investors' behavior during financial crises (pp. 203-217). Elsevier. https://doi.org/10.1016/B978-0-12-811252-6.00010-4
12.  Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987–1007. https://doi.org/10.2307/1912773
13.  Fadlallah, B., Chen, B., Keil, A., & Príncipe, J. (2013). Weighted-permutation entropy: A complexity measure for time series incorporating amplitude information. Physical Review E, 87(2), 022911. https://doi.org/10.1103/PhysRevE.87.022911
14.  Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37(3), 424-438. https://doi.org/10.2307/1912791
15.  Hendershott, T., Jones, C. M., & Menkveld, A. J. (2011). Does algorithmic trading improve liquidity? The Journal of Finance, 66(1), 1–33. https://doi.org/10.1111/j.1540-6261.2010.01624.x
 
16.  Hou, Y., Liu, F., Gao, J., Cheng, C., & Song, C. (2017). Characterizing complexity changes in Chinese stock markets by permutation entropy. Entropy, 19(10), 514. https://doi.org/10.3390/e19100514
17.  Jacobsson, E. (2009). How to predict crashes in financial markets with the Log-Periodic Power Law [Master's thesis]. Department of Mathematics and Statistics, Stockholm University.
18.  Jiang, J., Shang, P., Zhang, Z., & Li, X. (2017). Permutation entropy analysis based on Gini-Simpson index for financial time series. Physica A: Statistical Mechanics and its Applications, 486, 273-283. https://doi.org/10.1016/j.physa.2017.05.042
19.  Mantegna, R. N. (1999). Hierarchical structure in financial markets. *The European Physical Journal B - Condensed Matter and Complex Systems, 11*(1), 193-197. https://doi.org/10.1007/s100510050929
20.  Mantegna, R. N., & Stanley, H. E. (1999). Introduction to econophysics: Correlations and complexity in finance. Cambridge University Press.
21.  Molnár, A., & Csiszárik-Kocsir, Á. (2023). Forecasting economic growth with V4 countries' composite stock market indexes: A Granger causality test. Acta Polytechnica Hungarica, 20(3), 135-154. https://doi.org/10.12700/APH.20.3.2023.3.8
22.  Morabito, F. C., Labate, D., La Foresta, F., Bramanti, A., Morabito, G., & Palamara, I. (2012). Multivariate multi-scale permutation entropy for complexity analysis of Alzheimer's disease EEG. Entropy, 14(7), 1186-1202. https://doi.org/10.3390/e14071186
23.  Obstfeld, M., Shambaugh, J. C., & Taylor, A. M. (2005). The trilemma in history: Tradeoffs among exchange rates, monetary policies, and capital mobility. The Review of Economics and Statistics, 87(3), 423-438. https://doi.org/10.1162/0034653054638300
24.  Patel, S. A., & Sarkar, A. (1998). Crises in developed and emerging stock markets. Financial Analysts Journal, 54(6), 50-61. https://doi.org/10.2469/faj.v54.n6.2221
25.  Reinhart, C. M., & Rogoff, K. S. (2009). This time is different. In This time is different: Eight centuries of financial folly. Princeton University Press.
26.  Ruiz, M. d. C., Guillamón, A., & Gabaldón, A. (2012). A new approach to measure volatility in energy markets. Entropy, 14(1), 74-91. https://doi.org/10.3390/e14010074
27.  Silva, F. N., Zhao, Y., Cardoso, M. F., Donges, J. F., Eroglu, D., Kurths, J., & Macau, E. E. N. (2021). Detecting climate teleconnections with Granger causality. Geophysical Research Letters, 48(18), e2021GL094707. https://doi.org/10.1029/2021GL094707
28.  Siokis, F. M. (2018). Credit market jitters in the course of the financial crisis: A permutation entropy approach in measuring informational efficiency in financial assets. Physica A: Statistical Mechanics and its Applications, 499, 266-275. https://doi.org/10.1016/j.physa.2017.12.130
29.  Soloviev, V. N., Bielinskyi, A., & Solovieva, V. (2019). Entropy analysis of crisis phenomena for DJIA index. In ICTERI Workshops (pp. 434-449).
30.  Sprott, J. C. (2003). Chaos and time-series analysis. Oxford University Press.
31.  Tank, A., Covert, I., Foti, N., Shojaie, A., & Fox, E. B. (2021). Neural Granger causality. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(8), 4267-4279. https://doi.org/10.1109/TPAMI.2021.3065601
32.  Yang, X., & Zhou, M. (2024). Time-varying entropy and financial instability during global shocks. Finance Research Letters, 55, 104782. https://doi.org/10.1016/j.frl.2023.104782
33.  Yin, Y., & Shang, P. (2014). Weighted multiscale permutation entropy of financial time series. Nonlinear Dynamics, 78, 2921-2939. https://doi.org/10.1007/s11071-014-1626-4
34.  Zanin, M., Zunino, L., Rosso, O. A., & Papo, D. (2012). Permutation entropy and its main biomedical and econophysics applications: A review. Entropy, 14(8), 1553-1577. https://doi.org/10.3390/e14081553
35.  Zeeman, E. C. (1976). Catastrophe theory. Scientific American, 234(4), 65-83. https://doi.org/10.1038/scientificamerican0476-65
36.  Zhao, X., Ji, M., Zhang, N., & Shang, P. (2020). Permutation transition entropy: Measuring the dynamical complexity of financial time series. Chaos, Solitons & Fractals, 139, 109962. https://doi.org/10.1016/j.chaos.2020.109962
37.  Zolghadr-Asli, B., Enayati, M., Pourghasemi, H. R., Naghdyzadegan Jahromi, M., & Tiefenbacher, J. P. (2021). Application of Granger-causality to study the climate change impacts on depletion patterns of inland water bodies. Hydrological Sciences Journal, 66(12), 1767-1776. https://doi.org/10.1080/02626667.2021.1962880
International Journal of Finance & Managerial Accounting

Articles in Press, Accepted Manuscript
Available Online from 24 May 2026