Prediction accuracy and sloppiness of log-periodic functions

TL;DR

This paper investigates the challenges in fitting log-periodic power-law functions to time series data, highlighting their inherent sloppiness, which affects the reliability of crash predictions and suggests current estimation methods may be overly optimistic.

Contribution

It provides a detailed analysis of the sloppiness in LPPL models, demonstrating its impact on the accuracy of crash time predictions and discussing necessary considerations for fitting procedures.

Findings

LPPL functions are highly sensitive to some parameter combinations

Predicting divergence time with LPPL is inherently uncertain

Current probabilistic estimation methods may be overly optimistic

Abstract

We show that log-periodic power-law (LPPL) functions are intrinsically very hard to fit to time series. This comes from their sloppiness, the squared residuals depending very much on some combinations of parameters and very little on other ones. The time of singularity that is supposed to give an estimate of the day of the crash belongs to the latter category. We discuss in detail why and how the fitting procedure must take into account the sloppy nature of this kind of model. We then test the reliability of LPPLs on synthetic AR(1) data replicating the Hang Seng 1987 crash and show that even this case is borderline regarding predictability of divergence time. We finally argue that current methods used to estimate a probabilistic time window for the divergence time are likely to be over-optimistic.