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

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