Comment on Recent Claims by Sornette and Zhou

Owing to a large number of press releases in which my work has been heavily cited in support of the recent SP500 prediction by Sornette and Zhou (SZ), I feel it necessary to comment on this work and their follow-up preprint [1]. The predictions by SZ regarding the future behaviour of in particular the SP500 has received quite some attention and a substantial part of the evidence presented supporting the predictions of SZ is based on my numerical analysis of the Nikkei in the period 1990-2000[9]. Hence, I feel urged to present my own view on the log-periodic power law (LPPL) analysis of the financial markets (FM) made by SZ and in particular on the claims of LPPL behaviour in the FM in general and the SP500 in particular as well as the predictions that SZ derive from their analysis. In 1996 and 1997 two groups independently proposed that power laws with complex exponents, e.g., p(t) ≈ A + B(t c − t) z + C(t c − t) z cos (ω log(t c − t) + φ) (1) were relevant modeling tools for the description of price p(t) increases a few years prior to very large crashes [3, 5]. The background for the original suggestion of LPPL signatures in the financial markets was an analogy between second order phase transitions and rupture, in this context a " rupture in market belief ". Furthermore, it was proposed that the domain of the power law exponent should not be restricted to real values only. Consequently, the analogy was not confined to a pure power law behaviour but allowed for a power law behaviour decorated by so-called log-periodic oscillations, retrospectively to be seen as a quite provocative claim [8]. Disregarding the rupture analogy (for which the empirical evidence is scarce), one may also consider the proposed frame work simply as an Ansatz dF (x) d log x = αF (t) + higher order terms (2) for the dynamical rescaling of a price (or some related quantity) F (x) as a function of " time to the crash " x = t c − t. Such an Ansatz approach is not uncommon in the field of critical phenomena. Before commenting further on the recent claims by SZ, I should stress that the present author with D. Sornette in [7] has presented a synthesis of two independent research directions, namely that of LPPL analysis …