Bayesian Smoothing and Risk Analysis of Multivariate Models

• Activity Number: 112
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Risk Analysis
• Author(s): Dongchu Sun*+ and Shawn Ni and Paul L. Speckman
• Companies: University of Missouri-Columbia and University of Missouri and University of Missouri
• Keywords: Multivariate Smoothing ; Smoothing Spline ; GCV and GML ; Finantial Analysis ; Macroeconomics ; Time series

Abstract

The problem of spline smoothing has been thoroughly studied for univariate models. A number of authors have considered restricted versions of multivariate smoothing splines with multivariate dependent variables. Yee & Wild (1996) related multivariate spline model to generalized additive models and provided an algorithm for parameter estimation. Fessler (1991) proposed a GCV (generalized cross validation) estimate of the smoothing parameter of multivariate splines, and Wang et al. (2000) proposed GCV and GML estimate of smoothing parameters of a bivariate spline. In the literature, the multivariate signal processes are often assumed to be independent. In applications of multivariate models, the components of the multivariate function g(t) may be influenced by common factors. The smooth (signal) components are often correlated. For instance, economic theory suggests that the macroeconomic variables such as GDP and private investment have correlated trends. Restricting independence of the signal processes is inadvisable under such a scenario.

In this talk, joint smoothing is considered for multivariate models with correlated error components and correlated derivatives of the cu