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MARM Processes Part II: The Empirically-Based Subclass

Author

Listed:
  • Benjamin Melamed

    (Rutgers University)

  • Xiang Zhao

    (Rutgers University)

Abstract

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.

Suggested Citation

  • Benjamin Melamed & Xiang Zhao, 2013. "MARM Processes Part II: The Empirically-Based Subclass," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 37-83, March.
    • Handle: RePEc:spr:metcap:v:15:y:2013:i:1:d:10.1007_s11009-011-9210-6
    DOI: 10.1007/s11009-011-9210-6
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    References listed on IDEAS

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    1. Benjamin Melamed, 1991. "TES: A Class of Methods for Generating Autocorrelated Uniform Variates," INFORMS Journal on Computing, INFORMS, vol. 3(4), pages 317-329, November.
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