Extreme events from the return-volume process: a discretization approach for complexity reduction

We propose the discretization of real-valued financial time series into few ordinal values and use sparse Markov chains within the framework of generalized linear models for such categorical time series. The discretization operation causes a large reduction in the complexity of the data. We analyse daily return and volume data and estimate the probability structure of the process of lower extreme, upper extreme and the complementary usual events. Knowing the whole probability law of such ordinalvalued vector processes of extreme events of return and volume allows us to quantify non-linear associations. In particular, we find a new kind of asymmetry in the return - volume relationship. Estimated probabilities are also used to compute the MAP predictor whose power is found to be remarkably high.