Concurrent processing of heteroskedastic vector-valued mixture density models

Abstract

We introduce a combined two-stage least-squares (2SLS)–expectation maximization (EM) algorithm for estimating vector-valued autoregressive conditional heteroskedasticity models with standardized errors generated by Gaussian mixtures. The procedure incorporates the identification of the parametric settings as well as the estimation of the model parameters. Our approach does not require a priori knowledge of the Gaussian densities. The parametric settings of the 2SLS_EM algorithm are determined by the genetic hybrid algorithm (GHA). We test the GHA-driven 2SLS_EM algorithm on some simulated cases and on international asset pricing data. The statistical properties of the estimated models and the derived mixture densities indicate good performance of the algorithm. We conduct tests on a massively parallel processor supercomputer to cope with situations involving numerous mixtures. We show that the algorithm is scalable.

Keywords:

• vector-valued ARCH processes
• mixture densities
• geno-mathematical monitoring
• parallel programming
• high-performance computing

Acknowledgements

We are grateful to the experts at the CSC (Helsinki) for their advice in parallel computing techniques. Detailed comments and suggestions from anonymous referees are gratefully acknowledged.

Notes

. The third and fourth equalities follow since, by definition, all matrices are symmetric and the matrices and commute, , hence also and commute.