Detecting market crashes by analysing long-memory effects using high-frequency data

It is well known that returns for financial data sampled with high frequency exhibit memory effects, in contrast to the behavior of the much celebrated log-normal model. Herein, we analyse minute data for several stocks over a seven-day period which we know is relevant for market crash behavior in the US market, March 10-18, 2008. We look at the relationship between the Lévy parameter α characterizing the data and the resulting H parameter characterizing the self-similar property. We give an estimate of how close this model is to a self-similar model.