{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T15:13:22Z","timestamp":1761664402235,"version":"build-2065373602"},"reference-count":67,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,17]],"date-time":"2022-04-17T00:00:00Z","timestamp":1650153600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Stock markets can become inefficient due to calendar anomalies known as the day-of-the-week effect. Calendar anomalies are well known in the financial literature, but the phenomena remain to be explored in econophysics. This paper uses multifractal analysis to evaluate if the temporal dynamics of market returns also exhibit calendar anomalies such as day-of-the-week effects. We apply multifractal detrended fluctuation analysis (MF-DFA) to the daily returns of market indices worldwide for each day of the week. Our results indicate that distinct multifractal properties characterize individual days of the week. Monday returns tend to exhibit more persistent behavior and richer multifractal structures than other day-resolved returns. Shuffling the series reveals that multifractality arises from a broad probability density function and long-term correlations. The time-dependent multifractal analysis shows that the Monday returns\u2019 multifractal spectra are much wider than those of other days. This behavior is especially persistent during financial crises. The presence of day-of-the-week effects in multifractal dynamics of market returns motivates further research on calendar anomalies for distinct market regimes.<\/jats:p>","DOI":"10.3390\/e24040562","type":"journal-article","created":{"date-parts":[[2022,4,18]],"date-time":"2022-04-18T04:21:28Z","timestamp":1650255688000},"page":"562","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A New Look at Calendar Anomalies: Multifractality and Day-of-the-Week Effect"],"prefix":"10.3390","volume":"24","author":[{"given":"Darko","family":"Stosic","sequence":"first","affiliation":[{"name":"Centro de Inform\u00e1tica, Universidade Federal de Pernambuco, Av. Luiz Freire s\/n, Recife 50670-901, PE, Brazil"}]},{"given":"Dusan","family":"Stosic","sequence":"additional","affiliation":[{"name":"Centro de Inform\u00e1tica, Universidade Federal de Pernambuco, Av. Luiz Freire s\/n, Recife 50670-901, PE, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1183-7941","authenticated-orcid":false,"given":"Irena","family":"Vodenska","sequence":"additional","affiliation":[{"name":"Department of Administrative Sciences, Metropolitan College, Boston University, 1010 Commonwealth Avenue, Boston, MA 02215, USA"}]},{"given":"H. Eugene","family":"Stanley","sequence":"additional","affiliation":[{"name":"Center for Polymer Studies, Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA 02215, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5691-945X","authenticated-orcid":false,"given":"Tatijana","family":"Stosic","sequence":"additional","affiliation":[{"name":"Departamento de Estat\u00edstica e Inform\u00e1tica, Universidade Federal Rural de Pernambuco, Rua Dom Manoel de Medeiros s\/n, Dois Irm\u00e3os, Recife 52171-900, PE, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"75","DOI":"10.2469\/faj.v51.n1.1861","article-title":"Random Walks in Stock Market Prices","volume":"51","author":"Fama","year":"1995","journal-title":"Financ. Anal. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1111\/j.1540-6261.1970.tb00518.x","article-title":"Efficient capital markets: A review of theory and empirical work","volume":"25","author":"Malkiel","year":"1970","journal-title":"J. Financ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1093\/rfs\/1.1.41","article-title":"Stock market prices do not follow random walks: Evidence from a simple specification test","volume":"1","author":"Lo","year":"1988","journal-title":"Rev. Financ. Stud."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1111\/j.1467-6419.2009.00611.x","article-title":"The evolution of stock market efficiency over time: A survey of the empirical literature","volume":"25","author":"Lim","year":"2011","journal-title":"J. Econ. Surv."},{"key":"ref_5","first-page":"121","article-title":"Testing the weak form of efficient market hypothesis: Empirical evidence from Asia-Pacific markets","volume":"58","author":"Hamid","year":"2017","journal-title":"Int. Res. J. Financ. Econ."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.econlet.2009.01.028","article-title":"Measuring the degree of time varying market inefficiency","volume":"103","author":"Ito","year":"2009","journal-title":"Econ. Lett."},{"key":"ref_7","first-page":"1","article-title":"Market efficiency, market anomalies, causes, evidences, and some behavioral aspects of market anomalies","volume":"2","author":"Latif","year":"2011","journal-title":"Res. J. Financ. Account."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/0304-405X(80)90021-5","article-title":"Stock returns and the weekend effect","volume":"8","author":"French","year":"1980","journal-title":"J. Financ. Econ."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/BF02744521","article-title":"The day of the week effect on stock market volatility","volume":"25","author":"Berument","year":"2001","journal-title":"J. Econ. Financ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.frl.2016.09.006","article-title":"The day-of-the-week effects of stock markets in different countries","volume":"20","author":"Zhang","year":"2017","journal-title":"Financ. Res. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/S1058-3300(03)00038-7","article-title":"The day of the week effect on stock market volatility and volume: International evidence","volume":"12","author":"Kiymaz","year":"2003","journal-title":"Rev. Financ. Econ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/0304-405X(87)90066-3","article-title":"A monthly effect in stock returns","volume":"18","author":"Ariel","year":"1987","journal-title":"J. Financ. Econ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"49","DOI":"10.2469\/faj.v64.n2.11","article-title":"Equity Returns at the Turn of the Month","volume":"64","author":"McConnell","year":"2008","journal-title":"Financ. Anal. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/S1057-5219(03)00007-3","article-title":"The turn-of-the-month effect still lives: The international evidence","volume":"12","author":"Kunkel","year":"2003","journal-title":"Int. Rev. Financ. Anal."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.intfin.2013.12.002","article-title":"New evidence on turn-of-the-month effects","volume":"29","author":"Sharma","year":"2014","journal-title":"J. Int. Financ. Mark. Inst. Money"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/0304-405X(83)90029-6","article-title":"The anomalous stock market behavior of small firms in January: Empirical tests for tax-loss selling effects","volume":"12","author":"Reinganum","year":"1983","journal-title":"J. Financ. Econ."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1743","DOI":"10.1093\/rof\/rfs035","article-title":"Are monthly seasonals real? A three century perspective","volume":"17","author":"Zhang","year":"2013","journal-title":"Rev. Financ."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/ijfe.142","article-title":"Month of the year effect and January effect in pre-WWI stock returns: Evidence from a non-linear GARCH model","volume":"6","author":"Choudhry","year":"2001","journal-title":"Int. J. Financ. Econ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"78","DOI":"10.2469\/faj.v62.n5.4284","article-title":"The january effect","volume":"62","author":"Haug","year":"2006","journal-title":"Financ. Anal. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1611","DOI":"10.1111\/j.1540-6261.1990.tb03731.x","article-title":"High Stock Returns before Holidays: Existence and Evidence on Possible Causes","volume":"45","author":"Ariel","year":"1990","journal-title":"J. Financ."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1226","DOI":"10.1016\/j.jimonfin.2005.08.015","article-title":"Pre-holiday effects: International evidence on the decline and reversal of a stock market anomaly","volume":"24","author":"Chong","year":"2005","journal-title":"J. Int. Money Financ."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"835","DOI":"10.1016\/j.jbankfin.2011.09.014","article-title":"Fast profits: Investor sentiment and stock returns during Ramadan","volume":"36","author":"Etebari","year":"2012","journal-title":"J. Bank. Financ."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.jempfin.2003.01.002","article-title":"Pre-holiday effect, large trades and small investor behaviour","volume":"11","author":"Meneu","year":"2004","journal-title":"J. Empir. Financ."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"67","DOI":"10.2469\/faj.v29.n6.67","article-title":"The Behavior of Stock Prices on Fridays and Mondays","volume":"29","author":"Cross","year":"1973","journal-title":"Financ. Anal. J."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1463","DOI":"10.1016\/0378-4266(95)00054-2","article-title":"The day-of-the-week effect: The international evidence","volume":"20","author":"Dubois","year":"1996","journal-title":"J. Bank. Financ."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.qref.2017.02.009","article-title":"Seasonal anomalies in advanced emerging stock markets","volume":"66","author":"Seif","year":"2017","journal-title":"Q. Rev. Econ. Financ."},{"key":"ref_27","first-page":"53","article-title":"Day of the week effect on European stock markets","volume":"2","author":"Apolinario","year":"2006","journal-title":"Int. Res. J. Financ. Econ."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.ribaf.2004.02.004","article-title":"The day-of-the-week effect in foreign exchange markets: Multi-currency evidence","volume":"18","author":"Yamori","year":"2004","journal-title":"Res. Int. Bus. Financ."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.jeconbus.2016.04.001","article-title":"Revisiting calendar anomalies: Three decades of multicurrency evidence","volume":"86","author":"Kumar","year":"2016","journal-title":"J. Econ. Bus."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"23","DOI":"10.2307\/2331241","article-title":"Day-of-the-Week Effects in Financial Futures: An Analysis of GNMA, T-Bond, T-Note, and T-Bill Contracts","volume":"26","author":"Johnston","year":"1991","journal-title":"J. Financ. Quant. Anal."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.eneco.2014.02.005","article-title":"Daily seasonality in crude oil returns and volatilities","volume":"43","author":"Auer","year":"2014","journal-title":"Energy Econ."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1111\/j.1467-629X.2012.00497.x","article-title":"Weekend gold returns in bull and bear markets","volume":"53","author":"Blose","year":"2013","journal-title":"Account. Financ."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1016\/j.frl.2018.11.012","article-title":"The day of the week effect in the cryptocurrency market","volume":"31","author":"Caporale","year":"2019","journal-title":"Financ. Res. Lett."},{"key":"ref_34","first-page":"808","article-title":"A brief history and recent developments in day-of-the-week effect literature","volume":"37","author":"Philpot","year":"2011","journal-title":"Manag. Financ."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1108\/AJB-08-2017-0020","article-title":"Persistence of calendar anomalies: Insights and perspectives from literature","volume":"33","author":"Tadepalli","year":"2018","journal-title":"Am. J. Bus."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/S0378-4371(00)00271-5","article-title":"Statistical physics in foreign exchange currency and stock markets","volume":"285","author":"Ausloos","year":"2000","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/S0378-4371(02)01996-9","article-title":"Scaling behaviors in differently developed markets","volume":"324","author":"Matteo","year":"2003","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1209\/epl\/i2003-00194-y","article-title":"Multifractal properties of price fluctuations of stocks and commodities","volume":"61","author":"Matia","year":"2003","journal-title":"Europhys. Lett."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/j.chaos.2007.07.091","article-title":"Multifractality and herding behavior in the Japanese stock market","volume":"40","author":"Cajueiro","year":"2009","journal-title":"Chaos Solitons Fractals"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1891","DOI":"10.1016\/j.physa.2010.01.007","article-title":"Complexity-entropy causality plane: A useful approach to quantify the stock market inefficiency","volume":"389","author":"Zunino","year":"2010","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"936","DOI":"10.1016\/j.eneco.2011.03.012","article-title":"Multiscale entropy analysis of crude oil price dynamics","volume":"33","author":"Martina","year":"2011","journal-title":"Energy Econ."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1104","DOI":"10.1016\/j.physa.2018.05.039","article-title":"Stock market as temporal network","volume":"506","author":"Zhao","year":"2018","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"046130","DOI":"10.1103\/PhysRevE.68.046130","article-title":"Topology of correlation-based minimal spanning trees in real and model markets","volume":"68","author":"Bonanno","year":"2003","journal-title":"Phys. Rev. E"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1016\/j.physa.2018.05.050","article-title":"Collective behavior of cryptocurrency price changes","volume":"507","author":"Stosic","year":"2018","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/j.physa.2018.10.019","article-title":"Econophysics and sociophysics: Their milestones & challenges","volume":"516","author":"Kutner","year":"2019","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0378-4371(02)01383-3","article-title":"Multifractal detrended fluctuation analysis of nonstationary time series","volume":"316","author":"Kantelhardt","year":"2002","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_47","first-page":"3","article-title":"A survey of the Monday effect literature","volume":"42","author":"Pettengill","year":"2003","journal-title":"Q. J. Bus. Econ."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1080\/1350485042000203797","article-title":"The disappearing day-of-the-week effect in the world\u2019s largest equity markets","volume":"11","author":"Kohers","year":"2004","journal-title":"Appl. Econ. Lett."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1111\/1468-5957.00404","article-title":"The Reversal of the Monday Effect: New Evidence from US Equity Markets","volume":"28","author":"Mehdian","year":"2001","journal-title":"J. Bus. Financ. Account."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"2171","DOI":"10.1111\/j.1540-6261.1997.tb02757.x","article-title":"A new look at the Monday effect","volume":"52","author":"Wang","year":"1997","journal-title":"J. Financ."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1111\/j.1468-5957.1993.tb00299.x","article-title":"Good news, bad news, volume, and the Monday effect","volume":"20","author":"Fishe","year":"1993","journal-title":"J. Bus. Financ. Account."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"7015721","DOI":"10.1155\/2018\/7015721","article-title":"Dynamical variety of shapes in financial multifractality","volume":"2018","author":"Kowalski","year":"2018","journal-title":"Complexity"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.physa.2018.12.038","article-title":"Multifractal behavior of price and volume changes in the cryptocurrency market","volume":"520","author":"Stosic","year":"2019","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"2050076","DOI":"10.1142\/S0218348X20500760","article-title":"Multifractal analysis of Brazilian agricultural market","volume":"28","author":"Stosic","year":"2020","journal-title":"Fractals"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"3515","DOI":"10.1103\/PhysRevLett.67.3515","article-title":"Wavelets and multifractal formalism for singular signals: Application to turbulence data","volume":"67","author":"Muzy","year":"1991","journal-title":"Phys. Rev. Lett."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"011136","DOI":"10.1103\/PhysRevE.82.011136","article-title":"Detrending moving average algorithm for multifractals","volume":"82","author":"Gu","year":"2010","journal-title":"Phys. Rev. E"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"016103","DOI":"10.1103\/PhysRevE.74.016103","article-title":"Wavelet versus detrended fluctuation analysis of multifractal structures","volume":"74","year":"2006","journal-title":"Phys. Rev. E"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1140\/epjst\/e2007-00079-9","article-title":"Multifractal detrented fluctuation analysis of tonic-clonic epileptic seizures","volume":"143","author":"Figliola","year":"2007","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"20815","DOI":"10.1038\/srep20815","article-title":"Persistence in eye movement during visual search","volume":"6","author":"Amor","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1142\/S0218348X02001130","article-title":"Multifractal spectra as a measure of complexity in human posture","volume":"10","author":"Shimizu","year":"2002","journal-title":"Fractals"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1016\/j.physa.2015.02.034","article-title":"Power spectrum analysis and multifractal detrended fluctuation analysis of Earth\u2019s gravity time series","volume":"428","author":"Telesca","year":"2015","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"1052","DOI":"10.1016\/j.apenergy.2015.10.187","article-title":"Power spectrum and multifractal detrended fluctuation analysis of high-frequency wind measurements in mountainous regions","volume":"162","author":"Telesca","year":"2016","journal-title":"Appl. Energy"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.physa.2015.02.055","article-title":"Multifractal analysis of managed and independent float exchange rates","volume":"428","author":"Stanley","year":"2015","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_64","first-page":"433","article-title":"The Week-End Effect in Common Stock Returns: The International Evidence","volume":"40","author":"Jaffe","year":"1985","journal-title":"J. Financ."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"28004","DOI":"10.1209\/0295-5075\/88\/28004","article-title":"The components of empirical multifractality in financial returns","volume":"88","author":"Zhou","year":"2009","journal-title":"EPL Europhys. Lett."},{"key":"ref_66","first-page":"60003","article-title":"Quantitative features of multifractal subtleties in time series","volume":"88","author":"Rak","year":"2010","journal-title":"EPL Europhys. Lett."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.chaos.2011.11.004","article-title":"Finite-size effect and the components of multifractality in financial volatility","volume":"45","author":"Zhou","year":"2012","journal-title":"Chaos Solitons Fractals"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/4\/562\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:55:37Z","timestamp":1760136937000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/4\/562"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,17]]},"references-count":67,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["e24040562"],"URL":"https:\/\/doi.org\/10.3390\/e24040562","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,4,17]]}}}