Parallel computing for mixed-stable modelling of large data sets

Abstract

In this paper, we develop efficient parallel algorithms for the statistical processing of large data sets. Namely, we parallelize the maximum likelihood method for the estimation of parameters of the mixed-stable model. This method is known to be very computationally demanding. Financial German DAX stock index data are used as empirical data in this work. Several hierarchical levels of parallelism were distinguished, analyzed and implemented using OpenMP and MPI library. Parallel performance tests were conducted on the IBM SP6 supercomputer. Obtained performance results show that implemented parallel algorithms are very efficient and scalable on distributed and shared memory systems. Speedups up to 800 times were obtained for 1024 parallel processes. Noticeably, our parallel application is able to efficiently utilize the Simultaneous multithreading (Intel Hyper-Threading) technology in modern processors. This research demonstrates that the application of modern parallel technologies allows a fast and accurate estimation of mixed-stable parameters even for large amounts of data and promotes a wider use of stable modelling for the statistical data processing.