Abstract
The Sornette–Ide differential equation of herding and rational trader behaviour together with very small random noise is shown to lead to crashes or bubbles where the price change goes to infinity after an unpredictable time. About 100 time steps before this singularity, a few predictable roughly log-periodic oscillations are seen. A statistical analysis of DJ, S&P and Sofix (the share index for Bulgaria) shows higher fluctuations in the Sofix. This is consistent with the assumption that higher noise levels lead to shorter times between crashes. The higher level of fluctuations for the Sofix is consistent with Maslov's results comparing share indices for emerging and established markets (Maslov 2001 Physica A 301 397) * Paper presented at Applications of Physics in Financial Analysis (APFA) 3, 5–7 December 2001, Museum of London, UK.
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