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MARM Processes Part I: General Theory

Author

Listed:
  • Benjamin Melamed

    (Rutgers University)

  • Xiang Zhao

    (Rutgers University)

Abstract

This paper introduces a new class of real vector-valued stochastic processes, called MARM (Multivariate Autoregressive Modular) processes, which generalizes the class of (univariate) ARM (Autoregressive Modular) processes. Like ARM processes, the key advantage of MARM processes is their ability to fit a strong statistical signature consisting of first-order and second-order statistics. More precisely, MARM processes exactly fit an arbitrary multi-dimensional marginal distribution and approximately fit a set of leading autocorrelations and cross-correlations. This capability appears to render the MARM modeling methodology unique in its ability to fit a multivariate model to such a class of strong statistical signatures. The paper describes the construction of two flavors of MARM processes, MARM + and MARM − , studies the statistics of MARM processes (transition structure and second order statistics), and devises MARM-based fitting and forecasting algorithms providing point estimators and confidence intervals. The efficacy of the MARM fitting and forecasting methodology will be illustrated on real-life data in a companion paper.

Suggested Citation

  • Benjamin Melamed & Xiang Zhao, 2013. "MARM Processes Part I: General Theory," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 1-35, March.
    • Handle: RePEc:spr:metcap:v:15:y:2013:i:1:d:10.1007_s11009-011-9209-z
    DOI: 10.1007/s11009-011-9209-z
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    References listed on IDEAS

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    1. Miron Livny & Benjamin Melamed & Athanassios K. Tsiolis, 1993. "The Impact of Autocorrelation on Queuing Systems," Management Science, INFORMS, vol. 39(3), pages 322-339, March.
    2. 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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