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Further properties of random orthogonal matrix simulation

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  • Ledermann, Daniel
  • Alexander, Carol

Abstract

Random orthogonal matrix (ROM) simulation is a very fast procedure for generating multivariate random samples that always have exactly the same mean, covariance and Mardia multivariate skewness and kurtosis. This paper investigates how the properties of parametric, data-specific and deterministic ROM simulations are influenced by the choice of orthogonal matrix. Specifically, we consider how cyclic and general permutation matrices alter their time-series properties, and how three classes of rotation matrices – upper Hessenberg, Cayley, and exponential – influence both the unconditional moments of the marginal distributions and the behaviour of skewness when samples are concatenated. We also perform an experiment which demonstrates that parametric ROM simulation can be hundreds of times faster than equivalent Monte Carlo simulation.

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  • Ledermann, Daniel & Alexander, Carol, 2012. "Further properties of random orthogonal matrix simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 83(C), pages 56-79.
    • Handle: RePEc:eee:matcom:v:83:y:2012:i:c:p:56-79
    DOI: 10.1016/j.matcom.2012.07.013
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    Cited by:

    1. Hanke, Michael & Penev, Spiridon & Schief, Wolfgang & Weissensteiner, Alex, 2017. "Random orthogonal matrix simulation with exact means, covariances, and multivariate skewness," European Journal of Operational Research, Elsevier, vol. 263(2), pages 510-523.
    2. Carol Alexander & Xiaochun Meng & Wei Wei, 2020. "Targetting Kollo Skewness with Random Orthogonal Matrix Simulation," Papers 2004.06586, arXiv.org, revised Sep 2021.
    3. Alexander, Carol & Meng, Xiaochun & Wei, Wei, 2022. "Targeting Kollo skewness with random orthogonal matrix simulation," European Journal of Operational Research, Elsevier, vol. 299(1), pages 362-376.
    4. Geyer, Alois & Hanke, Michael & Weissensteiner, Alex, 2014. "No-Arbitrage ROM simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 66-79.

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