MARM Processes Part II: The Empirically-Based Subclass

Benjamin Melamed, Xiang Zhao

Research output: Contribution to journalArticlepeer-review


MARM (Multivariate Autoregressive Modular) processes constitute a versatile class of multidimensional stochastic sequences which can exactly fit arbitrary multi-dimensional empirical histograms and approximately fit the leading empirical autocorrelations and cross-correlations. A companion paper (Part I) presented the general theory of MARM processes. This paper (Part II) proposes practical MARM modeling and forecasting methodologies of considerable generality, suitable for implementation on a computer. The purpose of Part II is twofold: (1) to specialize the general class of MARM processes to a practical subclass, called Empirically-Based MARM (EB-MARM) processes, suitable for modeling of empirical vector-valued time series, and devise the corresponding fitting and forecasting algorithms; and (2) to illustrate the efficacy of the EB-MARM fitting and forecasting algorithms. Specifically, we shall consider MARM processes with iid step-function innovation densities and distortions based on an empirical multi-dimensional histogram, as well as empirical autocorrelation and cross-correlation functions. Finally, we illustrate the efficacy of these methodologies with an example of a three-dimension time series vector, using a software environment, called MultiArmLab, which supports MARM modeling and forecasting.

Original languageEnglish (US)
Pages (from-to)37-83
Number of pages47
JournalMethodology and Computing in Applied Probability
Issue number1
StatePublished - Mar 2013

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)


  • EB-MARM fitting methodology
  • EB-MARM forecasting methodology
  • Empirically-based MARM processes
  • MARM processes

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