Joint and Conditional Transformed T−Mixture Models with Applications to Financial and Economic Data

Journal of Risk, Vol. 11, No. 3, Spring 2009

Posted: 9 Dec 2010 Last revised: 10 Feb 2011

See all articles by Craig A. Friedman

Craig A. Friedman

TIAA-CREF

Wenbo Cao

Standard & Poor's - Quantitative Analytics

Jinggang Huang

Standard & Poor's - Quantitative Analytics

Yangyong Zhang

Standard & Poor's - Quantitative Analytics

Date Written: December 9, 2008

Abstract

We estimate joint and conditional probability densities via a new hybrid approach that incorporates ideas from copula modeling and makes use of known analytic results involving the conditional distributions of multivariate random variables that have joint (usual) multivariate t or t−mixture distributions. Our method amounts to the application of t or t−mixture modeling in a special “working space” that is used in copula modeling. We also provide new simulation algorithms and describe numerical experiments, performed on accounting data, stock return data, and housing price data, in which we compare the performance of our method with a number of benchmark approaches.

Keywords: Copula, Conditional Probability Density, Gaussian Mixture Model, t−Mixture Model, Multivariate Probability Distribution, Multivariate t−Distribution, Arellano-Valle and Bolfarine’s Generalized t−distribution, Fat-Tailed, Simulation, Stock Return Distribution, Financial Data, Economic Data

Suggested Citation

Friedman, Craig A. and Cao, Wenbo and Huang, Jinggang and Zhang, Yangyong, Joint and Conditional Transformed T−Mixture Models with Applications to Financial and Economic Data (December 9, 2008). Journal of Risk, Vol. 11, No. 3, Spring 2009, Available at SSRN: https://ssrn.com/abstract=1722905

Craig A. Friedman (Contact Author)

TIAA-CREF ( email )

730 3rd Ave
New York, NY 10017
United States

Wenbo Cao

Standard & Poor's - Quantitative Analytics ( email )

55 Water Street
New York, NY 10041
United States

Jinggang Huang

Standard & Poor's - Quantitative Analytics ( email )

55 Water Street
New York, NY 10041
United States

Yangyong Zhang

Standard & Poor's - Quantitative Analytics ( email )

55 Water Street
New York, NY 10041
United States

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