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

摘要: 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 ``anti-bubbles'' decelerating market devaluations following all-time highs. For this, we a simple dynamics model in which the demand decreases slowly barriers progressively quench in, leading power law decay price decorated log-periodic oscillations. document this on Japanese Nikkei stock index from 1990 present Gold future prices after 1980, both perform simultaneously parametric non-parametric analysis are fully consistent each other. extend approach next order perturbation, comparing fits one, two three log-frequencies, latter one providing prediction for general trend coming years. The spectrum shows existence log-periodicity high statistical significance, prefered scale ratio $\lambda \approx 3.5$ 1.9$ prices, comparable values obtained crashes.