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Recurrence Plot (RP) and Recurrence Quantification Analysis (RQA) are signal numerical analysis methodologies able to work with nonlinear dynamical systems and nonstationarity. Moreover, they well evidence changes in the states of a dynamical system. We recall their features and give practical recipes. It is shown that RP and RQA detect the critical regime in financial indices (in analogy with phase transition) before a bubble bursts, whence allowing to estimate the bubble initial time. The analysis is made on DAX and NASDAQ daily closing price between January 1998 and November 2003. DAX is studied in order to set-up overall considerations, and as a support for deducing technical rules. The NASDAQ bubble initial time has been estimated to be on 19 October 1999.
Fabretti et al. (Sun,) studied this question.