The prediction of the return period of the financial earthquake based on the Bayes’ Theorem

Abstract

Since the seismic behavior of the earth’s energy (which follows from the power law distribution) can be similarly seen in the energy realized by the stock markets, in this paper we consider a statistical study for comparing the (possible) financial crises and the earthquakes. For this end, the TP statistic, proposed by Pisarenko and et al. (2004), is employed for estimating the critical point or the lower threshold, i.e. the point beyond that the market energy follows from the power law (Pareto) distribution. The results confirm the deviation of the energy from the Pareto distribution in the high quantiles of the energy data. The upper threshold that the energy's distribution is changed from the Pareto to another distribution is also estimated by TP statistic. A simulation study is employed for checking out the statistical behavior of the estimated thresholds. The magnitude of the financial earthquakes is studied. The results indicate that the domestic and the international events have caused the financial earthquakes in Tehran Stock Exchange. Also, the positive relation between the daily energy released and the daily magnitude of the shocks that is connected by Gutenberg and Richter (1956) is confirmed. In addition, the return period of the next great financial earthquake is equal to 3.68 years.