The Continuous Hidden Threshold Mixed Skew-Symmetric Distribution

• Activity Number: 689
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Rachid Belhachemi*+ and Mohammed Bouaddi
• Companies: American University in Cairo and American University in Cairo
• Keywords: hidden, skew, symmetric

Abstract

In this paper we explore a way to construct a new family of univariate probability distribution where the parameters of the distribution capture the dependence between the variable of interest and the continuous latent state variable (the regime). The distribution nests two well -known families of distributions, namely, the skew normal family of Azzalini (1982) and a class of split distributions (Fernandez and Steel 1998) We provide a stochastic representation of the distribution which enables the user to easily simulate the data by just simulating from the uniform and the normal distributions. We also derive the moment generating function and the maximum likelihood estimation technique. The distribution comprises eight free parameters which makes it very flexible. This flexibility allows the user to capture many stylized facts about the data such as the excess volatility, regime dependence and asymmetry observed in financial data.