Generating random correlation matrices based on vines and extended onion method

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Generating random correlation matrices based on vines and extended onion method

TitleGenerating random correlation matrices based on vines and extended onion method
Publication TypeJournal Article
Year of Publication2009
AuthorsLewandowski, D, Kurowicka, D, Joe, H
JournalJournal of Multivariate Analysis
Volume100
Pagination1989-2001
Date PublishedOCT
Type of Articlearticle
ISSN0047-259X
KeywordsCorrelation matrix, Dependence vines, Onion method, Partial correlation
AbstractWe extend and improve two existing methods of generating random correlation matrices, the onion method of Ghosh and Henderson [S. Ghosh, S.C. Henderson, Behavior of the norta method for correlated random vector generation as the dimension increases, ACM Transactions on Modeling and Computer Simulation (TOMACS) 13 (3) (2003) 276-294] and the recently proposed method of Joe [H. Joe, Generating random correlation matrices based on partial correlations, journal of Multivariate Analysis 97 (2006) 2177-2189] based on partial correlations. The latteris based on the so-called D-vine. We extend the methodology to any regular vine and study the relationship between the multiple correlation and partial correlations on a regular vine. We explain the onion method in terms of elliptical distributions and extend it to allow generating random correlation matrices from the same joint distribution as the vine method. The methods are compared in terms of time necessary to generate 5000 random correlation matrices of given dimensions. (C) 2009 Elsevier Inc. All rights reserved.
DOI10.1016/j.jmva.2009.04.008