Applying Fully Bayesian Spline Smoothing to Estimate Yield Curves

• Activity Number: 681
• Type: Topic Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Xiaojun Tong*+ and Zhuoqiong He and Dongchu Sun and Shawn Ni
• Companies: University of Missouri-Columbia and University of Missouri-Columbia and University of Missouri and Univ of Missouri - Columbia
• Keywords: Smoothing Spline ; Nonparametric regression ; Bayesian Estimate ; Non-informative Prior ; Bayes factor

Abstract

In practice, one wants to estimate the yield curve for bonds. We adopt a fully Bayesian spline smoothing model proposed in Speckman and Sun (2003). We study this model with repeated observations. For the cubic smoothing spline, we derive the exactly formula for the precision matrix in the partially informative distribution. A Monte Carlo method for computing the joint posterior distribution, in particular, the Ratio-of-Uniforms method to sample from the marginal posterior density of the unknown smoothing parameter is applied. Numerical studies are given for illustration analyzing a real data set. Bayesian Factor is used to test if the response curve is polynomial or nonparametric.