Cubic splines have long been used to extract the discount, yield, and forward rate curves from coupon bond data. McCulloch used regression splines to estimate the discount function, and, more recently, Fisher, Nychka, and Zervos used smoothed splines, with the roughness penalty selected by generalized cross-validation, to estimate the forward rate curve. I propose using a smoothed spline but with a roughness penalty that can vary across maturities, to estimate the forward rate curve. This method is tested against the methods of McCulloch and Fisher, Nychka, and Zervos using monthly bond data from 1970 through 1995.
JEL classification: G12, C13
Key words: term structure, smoothing splines, generalized cross-validation
The author thanks Rob Bliss for his many helpful suggestions concerning variable roughness penalties and Mark Fisher for providing code and help in implementing the smoothed spline approach. The views expressed here are those of the author and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the author's responsibility.
Please address questions regarding content to Daniel F. Waggoner, Senior Quantitative Analyst, Federal Reserve Bank of Atlanta, 104 Marietta Street, N.W., Atlanta, Georgia 30303-2713, 404/498-8278, 404/498-8956 (fax), daniel.f. email@example.com.
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