**6. Conclusions**

In this article, the use of anomaly scores is illustrated for analyzing the cryptocurrency market. In addition to analyzing the volatility of the cryptocurrency market, anomaly scores of the market provide a complement to the analysis because anomalies are measured by deviation relative to variance and correlation. Specifically, robust Mahalanobis distance based on shrinkage estimators and minimum covariance determinant are shown to produce robust anomaly scores of cryptocurrencies that offer details of market anomalies that are not necessarily explained by standard volatility measures. With the use of anomaly scores as a complement to traditional volatility analyses, investment in cryptocurrencies can be further managed through a detailed understanding of normal or abnormal behavior of cryptocurrencies. Future research can be directed towards analyzing the underlying cause of the discrepancies between traditional volatility measures and the robust anomaly scores proposed in this study. One of the current shortcomings is the limited findings related to risk factors of cryptocurrencies and access to various data. Extended research into risk factors of cryptocurrencies will contribute to computing anomaly scores. Finally, further insight into abnormal behavior in cryptocurrencies will not only provide effective tools for managing investment in the crypto market but also become extremely valuable for investors expanding their assets with cryptocurrencies.

**Author Contributions:** Conceptualization, G.B. and J.H.K.; methodology, G.B. and J.H.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the BK21 FOUR (Fostering Outstanding Universities for Research) funded by the Ministry of Education (MOE, Korea) and the National Research Foundation of Korea (NRF), and partly supported by the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korean government (MSIT) (No.RS-2022-00155911, Artificial Intelligence Convergence Innovation Human Resources Development (Kyung Hee University)).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

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