Verification and Validation of Log-Periodic Power Law Models

TL;DR

This paper introduces a nonlinear verification and validation methodology for log-periodic power law models, assessing fitting procedures and addressing estimation issues in analyzing rare events across various domains.

Contribution

It develops a V&V approach for LPPL models, validating a specific algorithm and rejecting an unreliable estimation scheme, thus improving model reliability for rare event analysis.

Findings

Rejection of the exponential trend pre-conditioning estimation scheme

Validation of a subordinated algorithm that passes Feigenbaum's criticism

Enhanced reliability of LPPL models in analyzing rare events

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.