Verification and Validation of Log-Periodic Power Law Models

Abstract: We propose and implement a nonlinear Verification and Validation (V&V) methodology to test two fitting procedures for the log-periodic power law model (LPPL), a model that has diverse applications across data analysis, but known estimation issues. Prior studies have focused on ex-post analyses of rare events: Earthquakes, glacial break-off events, and financial crashes. Or, on non-dynamical simulations such as additive noise or resampling. Our results reject an estimation scheme that pre-conditions observed data by fitting and removing an exponential trend. We validate a subordinated algorithm, and confirm that it passes Feigenbaum's criticism, which articulates a broad hurdle for ex-post statistical learning from rare events.