Financial ``Anti-Bubbles'': Log-Periodicity in Gold and Nikkei collapses

TL;DR

This paper introduces a model explaining 'anti-bubbles' in financial markets, characterized by decelerating devaluations after peaks, supported by empirical analysis of Nikkei and Gold prices showing log-periodic patterns.

Contribution

It proposes a simple market dynamics model for anti-bubbles and demonstrates its validity through detailed analysis of Nikkei and Gold market data.

Findings

Log-periodic deceleration observed in Nikkei and Gold prices

Statistically significant log-periodic oscillations with specific scale ratios

Model predictions extend to future market trend analysis

Abstract

We propose that imitation between traders and their herding behaviour not only lead to speculative bubbles with accelerating over-valuations of financial markets possibly followed by crashes, but also to ``anti-bubbles'' with decelerating market devaluations following all-time highs. For this, we propose a simple market dynamics model in which the demand decreases slowly with barriers that progressively quench in, leading to a power law decay of the market price decorated by decelerating log-periodic oscillations. We document this behaviour on the Japanese Nikkei stock index from 1990 to present and on the Gold future prices after 1980, both after their all-time highs. We perform simultaneously a parametric and non-parametric analysis that are fully consistent with each other. We extend the parametric approach to the next order of perturbation, comparing the log-periodic fits with one, two and three log-frequencies, the latter one providing a prediction for the general trend in the coming years. The non-parametric power spectrum analysis shows the existence of log-periodicity with high statistical significance, with a prefered scale ratio of $\lambda \approx 3.5$ for the Nikkei index $\lambda \approx 1.9$ for the Gold future prices, comparable to the values obtained for speculative bubbles leading to crashes.