Forbidden patterns, permutation entropy and stock market inefficiency

Zunino, Luciano; Zanin, Massimiliano; Tabak, Benjamin M.; Pérez, Darío G.; Rosso, Osvaldo A.

doi:10.1016/j.physa.2009.03.042

Cited by 249Complex Systems and Time Series AnalysisFinancial Markets and Investment StrategiesStock Market Forecasting Methods

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Forbidden patterns, permutation entropy and stock market inefficiency

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Zunino, Luciano, Zanin, Massimiliano, Tabak, Benjamin M., Pérez, Darío G., Rosso, Osvaldo A.·2009·Physica A Statistical Mechanics and its Applications

DOI 10.1016/j.physa.2009.03.042

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To test the robustness of findings in relation to market maturity, the study also employs market maturity classifications provided by the Morgan Stanley Capital Index and the International Monetary Fund.
“To test the robustness of our findings in relation to market maturity, we also employ market maturity classifications provided by the Morgan Stanley Capital Index (MSCI) (Zunino et al., 2009) and the International Monetary Fund (IMF) (J. H. Kim & Shamsuddin, 2008).”
From Bridging the divide in financial market forecasting: machine learners vs. financial economists (2016) · cites this paper as Zunino et al., 2009

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Assessing sustainability in North America’s ecosystems using criticality and information theory
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Exploring disorder and complexity in the cryptocurrency space
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Information Entropy and Measures of Market Risk
Pele, D. T., Lazar, E., & Dufour, A. (2017) · Entropy · doi:10.3390/e19050226 · Cited by 46
“[3], since high values of entropy are related to randomness in the evolution of stock prices, according to the Efficient Market Hypothesis.”
Complexity analyses of multi-wing chaotic systems
He, S., Sun, K., & Zhu, C. (2013) · Chinese Physics B · doi:10.1088/1674-1056/22/5/050506 · Cited by 44
Anomaly Detection in Paleoclimate Records Using Permutation Entropy
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Fluctuation-based reverse dispersion entropy and its applications to signal classification
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Markov modeling via ordinal partitions: An alternative paradigm for network-based time-series analysis
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A maximum entropy method to assess the predictability of financial and commodity prices
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Characterizing Complexity Changes in Chinese Stock Markets by Permutation Entropy
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The experimental signals analysis for bubbly oil-in-water flow using multi-scale weighted-permutation entropy
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Does the singular value decomposition entropy have predictive power for stock market? — Evidence from the Shenzhen stock market
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Sampling period, statistical complexity, and chaotic attractors
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Info-quantifiers’ map-characterization revisited
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An investigation of Forex market efficiency based on detrended fluctuation analysis: A case study for Iran
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Weighted permutation entropy based on different symbolic approaches for financial time series
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Permutation entropy: Influence of amplitude information on time series classification performance
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The Amigó paradigm of forbidden/missing patterns: a detailed analysis
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Intraday return inefficiency and long memory in the volatilities of forex markets and the role of trading volume
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A New Feature Extraction Method for Ship-Radiated Noise Based on Improved CEEMDAN, Normalized Mutual Information and Multiscale Improved Permutation Entropy
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Refined Composite Multiscale Fuzzy Dispersion Entropy and Its Applications to Bearing Fault Diagnosis
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“Mechanical [28], biomedical [29], economy [30], geophysics [31], hydrology [32] DE (1) Unlike SE, DE does not lead to undeﬁned results in short signals [33]; (2) DE is less susceptible to the effects of noise [7]; (3) unlike PE, DE considers amplitude values [18]; (4) DE addresses the issue of…”
Background
Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics
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Multiscale behavior of financial time series model from Potts dynamic system
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“Recently, some researches have been made to apply entropy to quantify market efficiency in foreign exchange and stock markets [33,45].”
Background
Permutation Entropy for Graph Signals
Fabila-Carrasco, J. S., Tan, C., & Escudero, J. (2022) · IEEE Transactions on Signal and Information Processing over Networks · doi:10.1109/tsipn.2022.3167333 · Cited by 30
Modeling the flow of information between financial time-series by an entropy-based approach
Benedetto, F., Mastroeni, L., & Vellucci, P. (2019) · Annals of Operations Research · doi:10.1007/s10479-019-03319-7 · Cited by 29
Order patterns, their variation and change points in financial time series and Brownian motion
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Crude oil market efficiency: An empirical investigation via the Shannon entropy
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Interacting price model and fluctuation behavior analysis from Lempel–Ziv complexity and multi-scale weighted-permutation entropy
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Monitoring the informational efficiency of European corporate bond markets with dynamical permutation min-entropy
Zunino, L., Bariviera, A. F., Guercio, M., Martínez, L. B., & Rosso, O. A. (2016) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2016.03.007 · Cited by 27
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Entanglement witness and linear entropy in an open system influenced by FG noise
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“Visualizations for multiscale patterns of FG noise were also used to obtain Tsallis permutation entropy [36].”
Method
NON-LINEAR TOOLS AND METHODOLOGICAL CONCERNS MEASURING HUMAN MOVEMENT VARIABILITY: AN OVERVIEW
Caballero, C., Barbado, D., & Hernández, F. J. M. (2014) · Dialnet (Universidad de la Rioja) · Cited by 24
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Permutation entropy of finite-length white-noise time series
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Spatiotemporal complexity of chaos in a phase-conjugate feedback laser system
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Gearbox fault diagnosis based on local mean decomposition, permutation entropy and extreme learning machine
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“PE has been widely used in numerous applications, such as electroencephalography (EEG) signals [13, 14], stock market analysis [15], and chatter detection in turning processes [16].”
Method
A singular value decomposition entropy approach for testing stock market efficiency
Álvarez‐Ramírez, J., & Rodríguez, E. (2021) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2021.126337 · Cited by 23
Forecasting the crude oil prices based on Econophysics and Bayesian approach
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A novel hybrid feature extraction approach of marine vessel signal via improved empirical mode decomposition and measuring complexity
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Multiscale lead-lag relationships in oil and refined product return dynamics: A symbolic wavelet transfer entropy approach
Storhas, D. P., Mello, L. D., & Singh, A. K. (2020) · Energy Economics · doi:10.1016/j.eneco.2020.104927 · Cited by 22
Appropriate use of the increment entropy for electrophysiological time series
Liu, X., Wang, X., Zhou, X., & Jiang, A. (2018) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2018.01.009 · Cited by 23
Regularity in Stock Market Indices within Turbulence Periods: The Sample Entropy Approach
Olbryś, J., & Majewska, E. (2022) · Entropy · doi:10.3390/e24070921 · Cited by 21
“Specifically, high values of entropy are related to randomness in the evolution of stock prices [8].”
BackgroundMethod
High-frequency chaotic bursts in laser diode with optical-feedback
Malica, T., Bouchez, G., Wolfersberger, D., & Sciamanna, M. (2022) · Communications Physics · doi:10.1038/s42005-022-01052-5 · Cited by 21
The coupling impact of climate change on streamflow complexity in the headwater area of the northeastern Tibetan Plateau across multiple timescales
Shen, S., Song, C., Cheng, C., & Ye, S. (2020) · Journal of Hydrology · doi:10.1016/j.jhydrol.2020.124996 · Cited by 20
MaxEnt and dynamical information
Hernando, A., Plastino, A. R., & Plastino, A. R. (2012) · The European Physical Journal B · doi:10.1140/epjb/e2012-30009-3 · Cited by 20
Multifractal Analysis of Market Efficiency across Structural Breaks: Implications for the Adaptive Market Hypothesis
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“This fractal nature of the series was further established by Kantelhardt et al. (2002) and studied by Zunino et al. (2009).”
Background
Multiscale joint permutation entropy for complex time series
Yin, Y., Shang, P., Ahn, A. C., & Peng, C. (2018) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2018.09.179 · Cited by 19
An Entropy-Based Approach to Measurement of Stock Market Depth
Olbryś, J., & Ostrowski, K. (2021) · Entropy · doi:10.3390/e23050568 · Cited by 21
“High values of entropy are related to randomness in the evolution of stock prices [26].”
Background
Chaotic edge density fluctuations in the Alcator C-Mod tokamak
Zhu, Z., White, A. E., Carter, T. A., Baek, S. G., & Terry, J. L. (2017) · Physics of Plasmas · doi:10.1063/1.4978784 · Cited by 18
Refined composite multiscale weighted-permutation entropy of financial time series
Zhang, Y., & Shang, P. (2017) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2017.12.116 · Cited by 18
Complexity Changes in the US and China’s Stock Markets: Differences, Causes, and Wider Social Implications
Gao, J., Hou, Y., Fan, F., & Liu, F. (2020) · Entropy · doi:10.3390/e22010075 · Cited by 18
“While the finding that developed markets are more consistent with the EMH than the emerging ones [26] is very appealing, the reported PE value for emerging markets is actually very close to a scenario of complete randomness, which is 1.”
Background

Sử dụng hình mẫu khuyết và Entropy hoán vị để kiểm định tính hiệu quả thông tin trên thị trường chứng khoán của các quốc gia ASEAN
Tuấn, A. T. T. (2018) · Journal of Asian Business and Economic Studies · doi:10.24311/jabes/2018.29.11.696
Shannon entropy and high frequency financial time series
Shternshis, A. (2023) · Scuola Normale Superiore di Pisa · doi:10.25429/shternshis-andrey_phd2023-10-06
Is the US stock market becoming weakly efficient over time? Evidence from 80-year-long data
Álvarez‐Ramírez, J., Rodríguez, E., & Espinosa-Paredes, G. (2012) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2012.06.051 · Cited by 55
Determining Stock Market Changes using Permutation Entropy
Obanya, P. O., Olivier, C. P., & Verster, T. (2025) · Computational Economics · doi:10.1007/s10614-025-11198-3 · Cited by 2
A Measure of consistency between market efficiency and entropy of foreign exchange markets and stock markets
Gutiérrez, R. (2010)

Authors: Zunino, L., Zanin, M., Tabak, B. M., Pérez, D. G., & Rosso, O. A.
Affiliations: Consejo Nacional de Investigaciones Científicas y Técnicas (AR)
Universidad Autónoma de Madrid (ES)
Central Bank of Brazil (BR)
Universidad de Buenos Aires (AR)
Corresponding author: Zunino, Luciano
ORCID: Zunino, Luciano
Zanin, Massimiliano
Tabak, Benjamin M.
Rosso, Osvaldo A.
Venue: Physica A Statistical Mechanics and its Applications
Publisher: Elsevier BV
Published: 2009-07
Volume: 388
Issue: 14
Pages: 2854-2864
ISSN: 0378-4371 (ISSN-L)
DOI: 10.1016/j.physa.2009.03.042
OpenAlex: W2018876117
Cited by: 249
References: 55
Citations by year: 2026: 6 · 2025: 10 · 2024: 11 · 2023: 5 · 2022: 19 · 2021: 17 · 2020: 21 · 2019: 36 · 2018: 18 · 2017: 18 · 2016: 17 · 2015: 10 · 2014: 10 · 2013: 11 · 2012: 16
FWCI: 26.94
Type: journal article
Language: en
Open access: green
www.rcaap.pt
Licence: other-oa
www.elsevier.com/tdm/userlicense/1.0/ (tdm)
Locations: Physica A Statistical Mechanics and its Applications (publishedVersion)
Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) (publishedVersion, other-oa)
LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) (submittedVersion, cc-by-nc-nd)
RePEc: Research Papers in Economics (submittedVersion)
Americanae (AECID Library) (submittedVersion, other-oa)
LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) (submittedVersion, other-oa)
Funders: Consejo Nacional de Investigaciones Científicas y Técnicas
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Pontificia Universidad Católica de Valparaíso
Comisión Nacional de Investigación Científica y Tecnológica
Topics: Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Complex Systems and Time Series Analysis
Social Sciences › Economics, Econometrics and Finance › Finance › Financial Markets and Investment Strategies
Social Sciences › Decision Sciences › Management Science and Operations Research › Stock Market Forecasting Methods
Keywords: forbidden patterns, permutation entropy, time series complexity

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Forbidden patterns, permutation entropy and stock market inefficiency

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