**Predicting Equity Crises, Critical Exponents, And Earthquakes – II**

__Jan Dash __

Bloomberg LP

__Xipei Yang __

Bloomberg L.P.

July 19, 2016

**Abstract: **

We present further encouraging evidence for the Critical Exponent Earthquake Crisis (CEEC) Model that gives the probabilities of equity crises one year in advance. The CEEC model uses suitable precursor signals and is agnostic regarding dynamical origins of crises. The precursors accumulate in time between crises, like precursors to some earthquakes. The model uses a sophisticated noise filter to separate out crisis signals. The main metric is the anomalous exponent of an equity series describing the difference of the data variance scaling exponent from the Brownian variance scaling exponent of 1. No extra non-equity variables are used. The CEEC Model results for predicting crises are not perfect, but are much better than chance, including out-of-sample tests. The details here supplement our previous CEEC crisis paper (2013).

In another paper (2016) we give details showing that various markets – not just equities – that are already in crisis are on the average described by a critical exponent of the nonlinear-diffusion Reggeon Field Theory (RFT), calculated in 1974, with no free parameters. Nonlinear diffusion naturally extends Brownian motion. Rich/cheap crisis behavior is suggested as a paradigm. This supplements our previous CEEC crisis paper (2013).

The CEEC Model crisis predictions use the same scaling form described by the anomalous exponent as does the RFT. This consistency for crisis predictions and crisis behavior is significant.

### Predicting Equity Crises, Critical Exponents, And Earthquakes – II – Introduction

Previously we introduced the quantitative Critical Exponent Earthquake Crisis (CEEC) Model that gives the probability of an equity crisis one year in advance, and we analyzed the model with empirical evidence. In this paper we present further evidence.

Crises are often pictorially described by bubbles growing and collapsing. Our model predicts the collapse in advance. We call it the CEEC (Critical Exponent Earthquake Crisis) Model. The CEEC Model uses concepts of “critical exponents” from physics and also a qualitative analogy from the dynamics of earthquakes to describe the build-up of bubbles (increase of “frictional stress” or “precursors”) with subsequent crises from bubble collapses (“earthquakes”).

Sornette and collaborators have produced a crisis bubble model, which is different from the CEEC Model3. We discuss Sornette’s model and compare to some other work later in the paper.

The input to the CEEC model for an equity index is information drawn from the returns of that index using a sophisticated filter. No external information is used. That is, we do not consider the external environment to look for an “explanation” of the origins of a crisis.

The CEEC model probabilities can be a useful tool. The basic idea would be to provide early warning equity crisis signals to help prevent losses. The probability of crisis could also theoretically be used for Economic Capital, where risks are different in normal and crisis regimes.

Tests comparing the CEEC model to data4 yield encouraging results for overall back-fits, out-of-sample fits, and recent predictions, all much better than chance and also better than a refined Weibull benchmark. Table 1 below is the CEEC model “Box-Score” summary for the “rolling” out-of-sample crisis indicative tests for indices with 52 crises.

In Table 1 above, “Success Short Term” means the CEEC model successfully indicated the tested crisis one year in advance (71%), while “Short Term Type I Error” means that the model did not successfully indicate it (29%). “Success Long Term” means that the CEEC model did not indicate the tested crisis too early (0%), while “Type II Error” means that the model erroneously indicated it too early (0%).

### Note: Markets in Crisis and the Reggeon Field Theory

In a companion paper (Ref. i) we document behavior of various markets (FX, equities, commodities, rates, spreads) that are already in crisis. We find in-crisis behavior that is roughly consistent on average with that expected from a general theory of nonlinear diffusion, generalizing standard Brownian motion, the Reggeon Field Theory (RFT) iii. The empirical anomalous exponent giving the deviation from Brownian motion scaling exponent of 1 for variance, averaged over 200 cases and two different methodologies (linear and quadratic), is consistent with the RFT result for a critical exponent that was calculated by physicists in the 1970s, with no free parameters.

We propose that the RFT be viewed as a language for benchmark average dynamics past Brownian motion, including nonlinearities that can be seen in big moves during crises.

We also propose to characterize individual time series or market sectors as “rich” or “cheap” with respect to their scaling properties, to RFT which can serve as a theoretical benchmark for averages over all markets averaged over crises.

We view this result is consistent with, and lends credence to, the approach used here using anomalous exponents calculated in the same way, but in normal periods, to predict crises.

Ref i contains more results than our earlier summary paper (ref ii Error! Bookmark not efined.)

See full PDF below.