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

Abstract

A hypothesis is pursued that the financial log-periodicity, cascading self-similarity through various time scales, carries signatures of a law. It is shown that the most significant historical financial events can amazingly well be classified using a single and unique value of the preferred scaling factor λ = 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 a 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 has 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 logperiodic perspective is already of the same significance as the one of the early 1930s and of the late 1970s and (iii) all this points to a global much more serious crash at around 2025, of course from a level much higher (at least one order of magnitude) than in 2000.