Mining Stock Market Time Series and Modeling Stock Price Crash Using a Pretopological Framework.

We introduce a computational framework, namely a pretopological construct, for mining time series of stock prices in a financial market in order to expand a set of stocks by adding outside stocks whose average correlations with the inside are above a threshold. The threshold is considered as a function of the set’s size to verify the effect of group impact in a financial crisis. The efficiency of this approach is tested by a consecutive expansion process started from a single stock of Merrill Lynch & Co., which had a large influence in the United State market during the studying time. We found that the ability to imitate the real diffusion process can be classified into three cases according to the value of θ - a scaling constant of the threshold function. Finally, the process using pretopological framework is compared to a classical one, the minimum spanning tree of the corresponding stock network, showing its pertinence.