Log-periodic self-similarity: an emerging financial law?

Details Log-periodic self-similarity: an emerging financial law? Log-periodic self-similarity: an emerging financial law?

2002-09-25

arxiv.org/abs/cond-mat/0209591v2

Physica A 324 (2003) 174-182

Physics

Condensed Matter

Statistical Mechanics

Talk given by S. Drozdz at International Econophysics Conference, Bali, August 28-31, 2002; typos corrected

Scientific paper

10.1016/S0378-4371(02)01848-4

A hypothesis that the financial log-periodicity, cascading self-similarity through various time scales, carries signatures of a law is pursued. It is shown that the most significant historical financial events can be classified amazingly well using a single and unique value of the preferred scaling factor lambda=2, which indicates that its real value should be close to this number. This applies even to a declining decelerating log-periodic phase. Crucial in this connection is identification of a "super-bubble" (bubble on bubble) phenomenon. Identifying a potential "universal" preferred scaling factor, as undertaken here, may significantly improve the predictive power of the corresponding methodology. Several more specific related results include evidence that: (i) the real end of the high technology bubble on the stock market started (with a decelerating log-periodic draw down) in the begining of September 2000; (ii) a parallel 2000-2002 decline seen in the Standard & Poor's 500 from the log-periodic perspective is already of the same significance as the one of the early 1930s and of the late 1970s; (iii) all this points to a much more serious global crash in around 2025, of course from a level much higher (at least one order of magnitude) than in 2000.

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