Random orthogonal matrix simulation

Ledermann, Walter, Alexander, Carol and Ledermann, Daniel (2011) Random orthogonal matrix simulation. Linear Algebra and its Applications, 434 (6). pp. 1444-1467. ISSN 0024-3795

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Abstract

This paper introduces a method for simulating multivariate samples that have exact means, covariances, skewness and kurtosis. We introduce a new class of rectangular orthogonal matrix which is fundamental to the methodology and we call these matrices L matrices. They may be deterministic, parametric or data specific in nature. The target moments determine the L matrix then infinitely many random samples with the same exact moments may be generated by multiplying the L matrix by arbitrary random orthogonal matrices. This methodology is thus termed “ROM simulation”. Considering certain elementary types of random orthogonal matrices we demonstrate that they generate samples with different characteristics. ROM simulation has applications to many problems that are resolved using standard Monte Carlo methods. But no parametric assumptions are required (unless parametric L matrices are used) so there is no sampling error caused by the discrete approximation of a continuous distribution, which is a major source of error in standard Monte Carlo simulations. For illustration, we apply ROM simulation to determine the value-at-risk of a stock portfolio.

Item Type: Article
Additional Information: Simulation; Orthogonal matrix; Random matrix; Ledermann matrix; L matrices; Multivariate moments; Volatility clustering; Value-at-risk
Schools and Departments: School of Business, Management and Economics > Business and Management
Subjects: Q Science > QA Mathematics > QA0150 Algebra. Including machine theory, game theory
Q Science > QA Mathematics > QA0276 Mathematical statistics
Q Science > QA Mathematics > QA0076 Computer software
Related URLs:
Depositing User: Carol Alexander
Date Deposited: 11 Sep 2012 11:34
Last Modified: 11 Sep 2012 11:34
URI: http://sro.sussex.ac.uk/id/eprint/40628
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