Discriminating Market Anomalies Using Partitioned Local Depth: A Time Series Analysis of Flash Crashes and Structured Financial Events

Abstract Partitioned Local Depth (PaLD) is a nonparametric depth function that captures the local geometric structure of data. In this study, we investigate its effectiveness for distinguishing Flash Crash events from regular DOW30 market behavior using univariate financial time series from five major U.S. companies: Bank of America (BAC), International Business Machines (IBM), JPMorgan Chase (JPM), Walmart (WMT), and Exxon Mobil (XOM). For each time series, PaLD depth values were computed and summarized using nine statistical descriptors that characterize the underlying depth distribution. The resulting feature vectors were evaluated using Logistic Regression, Random Forest, Support Vector Machine, XGBoost, and Multilayer Perceptron classifiers under stratified five-fold cross-validation. To further assess the proposed framework, comparisons were conducted against established time series classification methods, including Dynamic Time Warping, Shapelet Transform, MiniROCKET, wavelet-based features, Gramian Angular Field with convolutional neural networks, Long Short-Term Memory networks, and a GAN-augmented convolutional neural network. Experimental results demonstrate that the proposed PaLD representation consistently achieves superior classification performance while remaining interpretable and computationally efficient. These findings highlight the potential of PaLD as an effective feature representation for financial time series classification and market anomaly detection.