The US 2000-2003 Market Descent: Clarifications

TL;DR

This paper defends previous findings on market descent patterns from critiques, clarifying methodological issues and emphasizing the universality of log-periodic power law signatures in financial crashes and anti-bubbles.

Contribution

It provides a detailed response to criticisms, clarifying key concepts and reinforcing the validity of log-periodic models in describing market crashes and anti-bubbles.

Findings

Log-periodic patterns are consistent in market crashes and anti-bubbles.

The analogy between rupture and crash is valid within the model.

Market descent exhibits fractal log-periodic power law behavior.

Abstract

In a recent comment (Johansen A 2003 An alternative view, Quant. Finance 3: C6-C7, cond-mat/0302141), Anders Johansen has criticized our methodology and has questioned several of our results published in [Sornette D and Zhou W-X 2002 The US 2000-2002 market descent: how much longer and deeper? Quant. Finance 2: 468-81, cond-mat/0209065] and in our two consequent preprints [cond-mat/0212010, physics/0301023]. In the present reply, we clarify the issues on (i) the analogy between rupture and crash, (ii) the Landau expansion, ``double cosine'' and Weierstrass-type solutions, (iii) the symmetry between bubbles and anti-bubbles and universality, (iv) the condition of criticality, (v) the meaning of ``bullish anti-bubbles'', (vi) the absolute value of t_c-t, (vii) the fractal log-periodic power law patterns, (viii) the similarity between the Nikkei index in 1990-2000 and the S&P500 in 2000-2002 and (ix) the present status of our prediction.