Prediction accuracy and sloppiness of log-periodic functions

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 the predictability of the 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.

Clarifications to questions and criticisms on the Johansen–Ledoit–Sornette financial bubble model

“…Having been developed over a decade ago, the JLS model has been studied, used and criticized by many researchers including Feigenbaum [45], Chang and Feigenbaum [46,47], van Bothmer and Meister [48], Fry [22], and Fantazzini and Geraskin [49]. The most recent papers addressing the pros and cons of past works on the JLS model are written by Bree and his collaborators [50,51]. Many ideas in these last two papers are correct, pointing out some of the inconsistencies in earlier works.…”

Multivariate bubbles and antibubbles

“…Equation (10) shows that an important feature of our model is that the hazard function remains bounded. This is in order to ensure that σ 2 (t) remains non-negative.…”

“…Equations (9)(10) show that specification of the hazard function h(t) completes the model. Equation (10) shows that an important feature of our model is that the hazard function remains bounded.…”

“…We note that from a mathematical perspective equation (10) holds some wider significance [18] since it satisfies a phase-transition condition delineating between random and deterministic behaviour in prices:…”

Lagrange Regularisation Approach to Compare Nested Data Sets and Determine Objectively Financial Bubbles' Inceptions

“…The filters used here are {(0.1 < m < 0.9), (6 < ω < 13), (t 2 − [t2 − t1] < t c < t 2 + [t2 − t1])}, so that only those calibrations that meet these conditions are considered valid and the others are discarded. These filters derive from the empirical evidence gathered in investigations of previous bubbles(Zhou and Sornette, 2003;Zhang et al, 2015;Sornette et al, 2015).Previous calibrations of the JLS model have further shown the value of additional constraints imposed on the nonlinear parameters in order to remove spurious calibrations (false positive identification of bubbles)Bree et al, 2013;Geraskin and Fantazzini, 2011). For our purposes, we do not consider them here.…”