Multiscale Permutation Entropy and Forbidden Patterns for Stock Market Volatility Analysis

Volatility forecasting is essential for risk management in financial markets. We present a multiscale framework combining permutation entropy and forbidden pattern analysis to detect nonlinear structures in high-frequency stock returns. By applying the method to S&P 500 and CSI 300 indices, we observed a 34% increase in detection sensitivity for volatility clustering compared with traditional GARCH models. The entropy-forbidden pattern coupling provided early-warning signals preceding volatility spikes during the 2008 financial crisis and 2015 China market crash. These results highlight the capacity of forbidden pattern analysis to capture hidden dynamics of market instability.