A Hybrid Model Based on Chaos Theory and Artificial Immune Systems for the Analysis and Classification of Stock Market Anomalies

Abstract

In this paper, a system for analyzing chaotic patterns in financial markets has been developed by combining classical chaos metrics with artificial immune systems for anomaly detection. Implemented indicators include the Lyapunov exponent, correlation dimension, approximate entropy, Hurst exponent, and the distance from a reference Lorenz trajectory. These metrics enable the detection of changes in market stability and predictability over time. An adaptive algorithm inspired by artificial immune systems was developed for identifying anomalous behaviors, adjusting detectors based on detected deviations. The results are presented through a series of interactive visualizations, including 3D plots, time series, and anomaly density maps. In addition to standard analysis, the system supports false alarm detection through controlled parameter variations. This approach provides deeper insights into the complex dynamics of financial markets and can serve as a tool for forecasting periods of instability.