**5. Conclusions**

Scholars could use data from stock markets all over the world to check whether the markets are e fficient, as well as find whether there is any market anomaly. When there is any anomaly being discovered, scholars first confirm the existence of the market anomaly and thereafter look for any existing model to explain the anomaly. If scholars cannot estimate, evaluate, and forecast any model to explain the anomaly, scholars will then explain the anomaly by using quantitative analysis, modeling, or even building up a new theory to explain the anomaly that built up the theory of Behavioral Finance. However, if there is any unexplained anomaly, one may grasp the methods to profiteer by using the anomaly. On the one hand, this is a good way to o ffer investors valuable investment advice. On the other hand, in the long run, these anomalies may disappear unconsciously.

Many studies, for example, Frankfurter and Mcgoun (2000), argue that numerous empirical researches are not consistent with the EMH, and they conclude that debate on Behavioral Finance is not rigorous enough. In this paper, we revisited the issue on market e fficiency and market anomalies. We first gave a brief review on market e fficiency, including discussing some theories for market efficiency and reviewing some important works in market e fficiency. We then reviewed di fferent market anomalies, including Winner–Loser E ffect, reversal e ffect, Momentum E ffect, calendar anomalies that include January e ffect, weekend e ffect and reverse weekend e ffect, book-to-market e ffect, value anomaly, size e ffect, Disposition E ffect, Equity Premium Puzzle, herd e ffect and ostrich e ffect, bubbles, and di fferent trading rules and technical analysis.

Thereafter, we reviewed di fferent theories of Behavioral Finance that could be used to explain market anomalies. Although we have discussed many studies on market e fficiency and anomalies, there are still many theoretical contributions in other areas that could also be useful to explain and interpret market e fficiency and anomalies. Readers may refer to Chang et al. (2016a, 2016b, 2016c, 2017, 2018) for contributions in other cognate areas that might be useful in theory and practice that related to market e fficiency and anomalies. Finally, we note that this review is useful to academics for their studies in EMH, anomalies, and Behavioral Finance; useful to investors for their decisions on their investment; and useful to policy makers in reviewing their policies in stock markets.

**Author Contributions:** Conceptualization, K.-Y.W., C.M., and W.-K.W.; writing—original draft preparation, K.-Y.W., C.M., and W.-K.W.; writing—review and editing, K.-Y.W., C.M., M.M., and W.-K.W.; supervision, K.-Y.W., M.M., and W.-K.W.; project administration, K.-Y.W. and W.-K.W. All authors have read and agreed to the published version of the manuscript.

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

**Acknowledgments:** For financial support, the third author wishes to thank the Australian Research Council and the National Science Council, Ministry of Science and Technology (MOST), Taiwan. The fourth author acknowledges the Research Grants Council of Hong Kong (Project Number 12500915), Ministry of Science and Technology, Taiwan (MOST, Project Numbers 106-2410-H-468-002 and 107-2410-H-468-002-MY3), Asia University, China Medical University Hospital, and Hang Seng Management College. The fourth author would also like to thank Robert B. Miller and Howard E. Thompson for their continuous guidance and encouragement.

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