Log-Periodic Crashes Revisited
We revisit the finding that crashes can be deterministic and governed by log-periodic formulas [D. Sornette, A. Johansen, Significance of log-periodic precursors to financial crashes, Quant. Finance 1 (2001) 452–471; D. Sornette, W.X. Zhou, The US 2000–2002 market descent: how much longer and deeper?, Quant. Finance 2 (2002) 468–481]. One- and two-harmonic equations are usually employed to fit daily data during bubble episodes. But a three-harmonics has been shown to fit anti-bubbles [A. Johansen, D. Sornette, Financial “anti-bubbles”: log-periodicity in gold and Nikkei collapses, Int. J. Mod. Phys. C 10 (1999) 563–575]. Here we show that the three-harmonic formula can work for bubble episodes as well as anti-bubbles. This is illustrated with daily data from the Brazilian real-US dollar exchange rate. And we also show that the three-harmonics can fit an intraday data set from that foreign exchange rate.
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- D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Papers cond-mat/0106520, arXiv.org.
- D. Sornette & W. -X. Zhou, 2002. "The US 2000-2002 Market Descent: How Much Longer and Deeper?," Papers cond-mat/0209065, arXiv.org.
- D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Quantitative Finance, Taylor & Francis Journals, vol. 1(4), pages 452-471.
- Didier Sornette & Wei-Xing Zhou, 2002. "The US 2000-2002 market descent: How much longer and deeper?," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 468-481.
- A. Johansen & D. Sornette, 1999. "Financial ``Anti-Bubbles'': Log-Periodicity in Gold and Nikkei collapses," Papers cond-mat/9901268, arXiv.org.
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