Spring Seminar Series - April 13, 2006
University of Minnesota
School of Statistics
College of Liberal Arts
Nonlinear
Properties of Conditional Log-returns Under Scale Mixtures
Venkata Krishna Jandhyala
Department of Statistics
Washington State University
Thursday, April 13, 2006
3:30 PM, 115
Ford Hall
Minneapolis, East Bank Campus
Social at 3:00 PM, 300 Ford Hall
Abstract
Analytical expressions are derived for the nonlinear regression and its
prediction error by modeling the log returns of financial assets as
scale mixtures of the multivariate normal distribution. The expressions
involve conditional moments of the mixing variable. These conditional
moments are explicitly derived when the mixing variable belongs to the
generalized inverse Gaussian (GIG) family, of which, gamma, inverse
gamma, and the inverse Gaussian distributions are members. The
effectiveness of the nonlinear model over the usual linear model is
captured through simulations for the above three families of
distributions. The proposed scale mixture models extend the arbitrage
pricing theory (APT) in financial modeling to non-Gaussian cases. The
methodology is applied to analyze the log returns intra-day data for
DELL, COKE and S&P 500 for the years 1998-2000.