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Nelson–Siegel, Affine and Quadratic Yield Curve Specifications: Which One is Better at Forecasting?


Ken Nyholm, European Insurance and Occupational Pension Authority, Westhafenplatz 1, 60327 Frankfurt am Main, Germany. E-mail:


In this paper we compare the in-sample fit and out-of-sample forecasting performance of no-arbitrage quadratic, essentially affine and dynamic Nelson–Siegel term structure models. In total, 11 model variants are evaluated, comprising five quadratic, four affine and two Nelson–Siegel models. Recursive re-estimation and out-of-sample 1-, 6- and 12-month-ahead forecasts are generated and evaluated using monthly US data for yields observed at maturities of 1, 6, 12, 24, 60 and 120 months. Our results indicate that quadratic models provide the best in-sample fit, while the best out-of-sample performance is generated by three-factor affine models and the dynamic Nelson–Siegel model variants. Statistical tests fail to identify one single best forecasting model class. Copyright © 2011 John Wiley & Sons, Ltd.