Original article: Further properties of random orthogonal matrix simulation

Authors:
Daniel Ledermann;Carol Alexander
Affiliations:
ICMA Centre, Henley Business School at Reading, Reading RG6 6BA, UK;School of Business, Management and Economics, University of Sussex, Falmer, Brighton, BN1 9SK, UK
Venue:
Mathematics and Computers in Simulation
Year:
2012

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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.