Evaluation and Prediction of Stock Market Crash Risk in Mexico Using Log-Periodic Power-Law Modeling

This study applies the Log-Periodic Power-Law (LPPL) framework to three major equity markets—Mexico (IPC), Brazil (IBOVESPA), and the United States (NYSE Composite)—using daily closes from 8 November 1991–30 January 2025 for IPC and NYSE, and 3 May 1993–30 January 2025 for IBOVESPA. Multi-window calibrations (L (Formula presented.) 180, 240, 300, 360, 420) are estimated in raw and log space to evaluate bubble signatures and the stability of the critical time (Formula presented.). Across all indices, log-space fits consistently outperform raw fits in terms of RMSE and (Formula presented.), and longer windows reduce parameter variability, yielding coherent clusters of (Formula presented.). Under full-sample conditions, the LPPL structure points to March–April 2025 for NYSE, mid-October 2025 for IBOVESPA, and October–December 2025 for IPC, while shorter windows pull (Formula presented.) forward. A rolling early-warning ensemble translates these estimates into lead-based risk bands, with numerical reporting used when median leads fall just outside the 60-trading-day decision horizon. The early-2025 weakening in the U.S. market is consistent with the NYSE cluster, whereas Brazil and Mexico remain within their projected windows as of September 2025. The analysis highlights the strengths of LPPL—behavioral interpretability and hazard-based framing—while noting limitations such as window sensitivity and parameter sloppiness, reinforcing the need for conservative communication and the use of longer-window weighting in practical applications.