Multifractal analysis and multiagent simulation for market crash prediction

In this paper the results of multifractal analysis by means of partitions and scaling function calculation are described, as well as wavelet analysis, which were applied to USA 1987 October Black Monday DJ data. For the partition calculation and Legendre transform a special program was elaborated. As our aim is predicting crash situations, we are trying to find out the best indicator that uses multifractal analysis and wavelet analysis methodology. With this aim in mind we have tested different methods of preprocessing the original time series to discover the best indicator. The wavelet analysis data were calculated on a 256 day moving window. The changes in the multifractal analysis features were studied while approaching crisis point and after the crisis. From the multiagent market model we can observe the crisis evolution and the dynamic of changing parameters such as share prices, trading volumes, price increments and statistical distribution dependent on traders' strategies.