Financial

Saint-Petersburg State University Faculty of Physics and DATAART company

Experimental Program of Supplementary Education "Information Technologies, Econophysics, and Complex Systems Management"

Internship Project

"Prediction of Crashes and Critical Points on the US Stock Market Using the Method of Modified Local Hölder Coefficients"

Accomplished by R.R. Schastlivtsev, A.M. Kuznetsov
Supervised by L.A. Dmitrieva

This paper is dedicated to elaboration and application of the special indicator based on the modified local Hölder coefficients used for prediction of the stock market crashes and critical points. The described method is based on the hypothesis that for some period of time before the critical point the characteristics of the financial series change becoming more regular.

This work describes the computational algorithm for calculation of the modified local Hölder coefficients and indicator based on these coefficients which allow to calculate the series’ smoothness locally. This method was tested on the artificial data of varying smoothness and it was shown that calculated modified local Hölder coefficients fluctuate close to their theoretical values.

Algorithm was tested on real financial data as well and it was shown that by distinguishing special areas (spikes) in the indicators behavior it is possible to forecast the critical points in the financial series, such as abrupt decreases and increases or changes of trend. Examination of the indicator behavior for 30 shares which make up the Dow Jones Industrial Average by the example of crises of 1987 and 2001 showed that elaborated indicator provides statistically significant forecasts of critical events and crashes of the stock markets.

Within the research framework the Analitic software application was developed. The application allows to calculate the modified local Hölder coefficients for specified time series. Basing on the calculated coefficients the application allows to forecast the potential critical points of the series. The application was developed on the .NET platform, in C#.