Examining the dynamical transition in the Dow Jones Industrial Index from Bull to Bear market using Recurrence Quantification Analysis

Abstract

We present evidence of phase transitions (periodic to chaotic and chaotic to chaotic) in the Dow Jones Industrial Index as it transitions from Bull to Bear market. There is also evidence of a completely unpredictable (i.e., nondeterministic) regime just as the market peaks. The noisy trader theory is suggested as the economic explanation for this unpredictability i.e. rational but uninformed traders chase noise rather than the usual macro economic and financial variables. We suggest that the collapse in determinism allows the dynamics of the market to break from the past and that the market is in fact piecewise deterministic. A principal component series is developed and named the random market indicator, (RMI). This can be used to indicate when the market is transitioning. The RMI indicator could be used by market participants, financial regulators and policy makers as an indicator of market crisis. During times of crises, quantitative risk estimation techniques such as stationary value at risk models, will give misleading results and should not be used.