Skewness-Corrected Copula-Based Outlier Detection for High-Frequency Financial Data from the Warsaw Stock Exchange

The objective of outlier detection is to identify rare events, i.e. the observations in empirical data that have significantly different feature values or different characteristics than the rest of observations. Therefore, it is of high importance to conduct the outlier detection in high-frequency financial data for achieving a good quality of empirical analyses, as well as the risk management and model fitting tasks. In our paper, we investigate the use of COPOD (Copula-Based Outlier Detection) – a parameter-free and interpretable anomaly detection algorithm based on application of empirical copulas and computation of the corresponding tail probabilities. This performance is assessed on real-world data from the Warsaw Stock Exchange (GPW). In our research, we follow the theoretical framework of Li et al. [10] and restate its core formulas in a concise notation adapted later to the chosen financial setting. We provide the Python implementation of a skewness-corrected version of COPOD, closely connected to the original algorithm, and employ it to the empirical dataset, which is a pre-processed feature set derived from the GPW tick dataset, collected in the GPW20230403000tind_for_COPOD.csv file. The empirical results show that the skewness-corrected COPOD algorithm successfully identifies extreme price and return observations in the selected data, while simultaneously remaining computationally efficient and easy to interpret method. Additionally, we also discuss practical implications of the conducted research and present possible directions and extensions of the study towards anomaly identification for the future work.