Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 4, Pages 393-410

Parallelization algorithms for modeling ARM processes

Benjamin Melamed and Santokh Singh

Rutgers University, Faculty of Management, Department of MSIS, 94 Rockafellar Rd., Piscataway, NJ 08854, USA

Received 1 March 2000; Revised 1 September 2000

Copyright © 2000 Benjamin Melamed and Santokh Singh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


AutoRegressive Modular (ARM) processes are a new class of nonlinear stochastic processes, which can accurately model a large class of stochastic processes, by capturing the empirical distribution and autocorrelation function simultaneously. Given an empirical sample path, the ARM modeling procedure consists of two steps: a global search for locating the minima of a nonlinear objective function over a large parametric space, and a local optimization of optimal or near optimal models found in the first step. In particular, since the first task calls for the evaluation of the objective function at each vector of the search space, the global search is a time consuming procedure. To speed up the computations, parallelization of the global search can be effectively used by partitioning the search space among multiple processors, since the requisite communication overhead is negligible.

This paper describes two space-partitioning methods, called Interleaving and Segmentation, respectively. The speedups resulting from these methods are compared for their performance in modeling real-life data.