Parallelization algorithms for modeling ARM processes

Benjamin Melamed, Santokh Singh

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)393-410
Number of pages18
JournalJournal of Applied Mathematics and Stochastic Analysis
Volume13
Issue number4
DOIs
StatePublished - 2001

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

Keywords

  • ARM Processes
  • Autocorrelation Function
  • Circulant Matrices
  • GSLO Algorithm
  • Optimization
  • Parallel Computation
  • Partitioning
  • Similarity Classes

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