Financial Anti-Bubbles Log-Periodicity in Gold and Nikkei Collapses

We propose that the herding behavior of traders leads not only 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 characterized by decelerating log-periodic oscillations. We document this behavior of the Japanese Nikkei stock index from 1990 to present and of the gold future prices after 1980, both after their all-time highs. We perform simultaneously parametric and nonparametric analyses 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 providing a prediction for the general trend in the coming years. The nonparametric power spectrum analysis shows the existence of log-periodicity with high statistical significance, with a preferred scale ratio of λ≈3.5 for the Nikkei index and λ≈1.9 for the Gold future prices, comparable to the values obtained for speculative bubbles leading to crashes.