The utility of hyperplane angle metric in detecting financial concept drift

Abstract

In financial time series analysis, introducing a new metric for concept drift is essential to address the limitations of existing evaluation methods, particularly in terms of speed, interpretability, and stability. Performance-based metrics and model-based metrics are the most commonly used to detect concept drift. For example, the error rate, which belongs to performance-based metric, is a frequently used metric that directly reflects the difference between the model’s output and the actual results, making it suitable for quick decision-making. Mahalanobis Distance, being a model-based metric, detects concept drift by evaluating deviations in the sample distribution, offering deeper interpretability and stability. Generally speaking, performance-based metrics excel in speed but lack deeper interpretability and stability, while model-based metrics are opposite. To achieve speed, deeper interpretability, and stability, we propose a novel metric termed the Angle Between Hyperplanes (ABH), which calculates the angle between earlier and later hyperplanes at two distinct time points through an arc-cosine function. This metric quantifies the similarity between two decision boundaries, with the angle reflecting the degree of concept drift detection. In other words, a larger angle indicates a higher probability of detecting concept drift. ABH offers good interpretability, as its angle has a geometric presentation, and it is time-efficient, requiring only the calculation of an arc-cosine function. To validate the effectiveness of the ABH, we integrate it into the Drift Detection Model (DDM) framework, replacing error rate-based metrics to monitor data distribution over time. Empirical studies on synthetic datasets show that ABH achieves approximately a 50% reduction in the Coefficient of Variation (Cv) compared to error rate-based approaches, demonstrating the stability of ABH. On the Shanghai and Shenzhen Stock Exchanges, our model outperforms the recent models. For instance, our model outperforms the Weighted Increment-Decrement Support Vector Machine (WIDSVM), reducing the error rate by 4% and 1%, respectively.