Predictive Modeling with Composite of Popular Distributions

• Activity Number: 30 - Bayesian Modeling and Time Series
• Type: Contributed
• Date/Time: Sunday, July 30, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Min Deng* and Mostafa S Aminzadeh
• Companies: Towson University and Towson University
• Keywords: MLE ; Bayesian inference ; composite density ; predictive density ; variable-at-risk ; conditional tail expectation

Abstract

Modeling based on data information is one of the most important research topics in finance and economic fields. In this article we consider the composite of two popular distributions in order to model the very heavy tail data. The maximum likelihood, smoothed empirical percentile, and Bayes estimates for the parameters are derived. A gamma distribution as a prior is used along with a Bayesian predictive density. Many important risk measures, such as Value-at-Risk (VaR) and Conditional Tail Expectation (CTE) are discussed. The important concepts, such as Limited VaR and Limited CTE are defined, derived and estimated based on the predictive distribution. Accuracy of the estimates of the parameters and the measures are assessed by simulation studies.