Multifractal analysis and instability index of prior-to-crash market situations

TL;DR

This paper uses multifractal analysis of market price signals to identify properties that characterize and predict market crashes, providing early warning indicators based on raw data.

Contribution

It introduces a novel application of multifractal spectra and an instability index to analyze prior-to-crash market conditions from raw price data.

Findings

Spectra exhibit properties indicative of impending crashes.

Instability index correlates with crash likelihood.

Method provides early warning signals for market crashes.

Abstract

We take prior-to-crash market prices (NASDAQ, Dow Jones Industrial Average) as a signal, a function of time, we project these discrete values onto a vertical axis, thus obtaining a Cantordust. We study said cantordust with the tools of multifractal analysis, obtaining spectra by definition and by lagrangian coordinates. These spectra have properties that typify the prior-to-crash market situation. Any of these spectra entail elaborate processing of the raw signal data. With the unprocessed raw data we obtain an instability index, also with properties that typify the prior-to-crisis market situation. Both spectra and the instability index agree in characterizing such crashes, and in giving an early warning of them.