Estimating Univariate Distributions Via Relative Entropy Minimization: Case Studies on Financial and Economic Data

International Journal of Theoretical and Applied Finance (IJTAF), 2010

Posted: 8 Jun 2010 Last revised: 9 Jun 2010

See all articles by Craig A. Friedman

Craig A. Friedman

TIAA-CREF

Yangyong Zhang

Standard & Poor's - Quantitative Analytics

Jinggang Huang

Standard & Poor's - Quantitative Analytics

Date Written: February 1, 2010

Abstract

We use minimum relative entropy (MRE) methods to estimate univariate probability density functions for a varied set of financial and economic variables, including S&P500 index returns, individual stock returns, power price returns and a number of housing-related economic variables. Some variables have fat tail distributions, others have finite support. Some variables have point masses in their distributions and others have multimodal distributions. We indicate specifically how the MRE approach can be tailored to the stylized facts of the variables that we consider and benchmark the MRE approach against alternative approaches. We find, for a number of variables, that the MRE approach outperforms the benchmark methods.

Keywords: Kullback-Leibler relative entropy, maximum likelihood, probability distribution, fat-tailed, point mass, stock return distribution, stock index return distribution, financial data, economic data, California Housing Data

Suggested Citation

Friedman, Craig A. and Zhang, Yangyong and Huang, Jinggang, Estimating Univariate Distributions Via Relative Entropy Minimization: Case Studies on Financial and Economic Data (February 1, 2010). International Journal of Theoretical and Applied Finance (IJTAF), 2010, Available at SSRN: https://ssrn.com/abstract=1621550

Craig A. Friedman (Contact Author)

TIAA-CREF ( email )

730 3rd Ave
New York, NY 10017
United States

Yangyong Zhang

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

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