Mixed-stable modeling of high-frequency financial data: parallel computing approach

Abstract

In this paper we apply the mixed-stable model for the analysis of high- frequency German DAX stock return data. We demonstrate the inadequacy of the classical Gaussian model as well as standard α-stable models. We develop efficient parallel numerical algorithms for the maximum likelihood estimation of mixed-stable parameters. The research has showed that the application of modern parallel technologies allows a fast estimation of mixed-stable parameters even for large amounts of data. We have studied the influence of the accuracy of probability density function calculation and maximum likelihood optimization on the results of the modelling and processing time and constructed mixed-stable models for all 29 DAX companies. The adequacy of the modelling was verified with Koutrouvelis goodness-of-fit test.