**5. Conclusions**

This paper investigated the multifractal behavior of the day-of-the-week returns for market indices worldwide. We applied the MF-DFA method to daily returns for each day of the week (Monday returns, Tuesday returns and so on) and calculated the multifractal spectra as well as their complexity parameters. Considering the multifractal parameters' positions of the maximum *α*0 and width W of an *f*(*α*) spectrum, we observed that distinct multifractal properties were found for the different days of the week, where North American, European and some Asian (South Korea, Indonesia and Hong Kong) and Latin American markets (Chile and Mexico) tended to show both stronger persistency (*<sup>α</sup>*0 > 0.5) and stronger multifractality (larger W) for the Monday returns, while for Australia, Indonesia and Taiwan, this tendency was found for the Tuesday returns. This finding agrees with the literature in that different day-of-the-week effects exist for different markets [25]. Some Asian markets displayed the Tuesday anomaly, being one day out of phase with the North American markets due to different time zones [64]. We found that multifractality arose from a broad probability density function and long-term correlations by analyzing shuffled series. The time-dependent multifractal analysis of the United States (GSPC) market revealed that the multifractal spectra for the Monday returns shifted to the left, or the fluctuations became less persistent over time. Other day-of-the-week returns exhibited small movements in the multifractal spectra. While the authors of [48] found that the effects from calendar anomalies vanished after 1980, in our study, we observed that the day-of-the-week effects persisted after the 1980s. Notably, the Monday returns exhibited much broader multifractal spectra compared with other days of the week. This behavior was especially pronounced around Black Monday on 19 October 1987 and the global financial crisis in 2008. A possible explanation for this phenomenon is the weekend gap in trading hours, leading to even more speculative behavior from investors during a crisis. Monday returns in general in the US tend to be different compared with those of other days of the week. This anomaly has been attributed to companies' release of news after the financial markets close on Friday, and hence, the Monday prices reflect the accumulated reaction of investors over the weekend. This unique behavior of financial asset prices on Monday can be informative and useful for investment decision making and can inform policymakers to possibly limit important news releases on Friday afternoon. The Monday effect may be reduced by current tendencies of after-hours trading. However, since the after-hours trading volumes are much lower than the regular trading hours, the Monday effect is still present. Future studies should further investigate the multifractal dynamics and day-of-the-week effects for other financial markets and extend the current analysis to other calendar anomalies.

**Author Contributions:** Data curation, D.S. (Darko Stosic); Formal analysis, D.S. (Dusan Stosic); Methodology, T.S.; Supervision, H.E.S.; Writing—review & editing, I.V. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
