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

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

1999-01-25

arxiv.org/abs/cond-mat/9901268v1

International Journal of Modern Physics C, Vol. 10, No. 4 (1999) 563-575

Physics

Condensed Matter

Statistical Mechanics

14 pages with 4 figures

Scientific paper

10.1142/S0129183199000437

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.

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