The arbitrage-free generalized Nelson–Siegel term structure model: does a good in-sample fit imply better out-of-sample forecasts?

Author Affiliation

Wali Ullah is Professor, Director CBER and Director ORIC Project at Institute of Business Administration (IBA), Karachi

Faculty / School

Faculty of Business Administration (FBA)


Department of Economics

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Empirical Economics




At the zero lower bound, the dynamic Nelson–Siegel (DNS) model and even the Svensson generalization of the model have trouble in fitting the short maturity yields and fail to grasp the characteristics of the Japanese government bonds (JGBs) yield curve. During the zero interest rate policy regime, the short end of the yield curve is flat and yields corresponding to various maturities have asymmetric movements. Therefore, closely related generalized versions of Nelson–Siegel model—with and without no-arbitrage restriction (GAFNS and GDNS)—that have two slopes and curvatures factors are considered and compared empirically in terms of in-sample fit as well as out-of-sample forecasts with the standard Nelson–Siegel model—with and without no-arbitrage restriction (AFNS and DNS). The affine-based models provide a more attractive fit of the yield curve than their counterpart DNS-based models. Both extended models are capable to restrict the estimated rates from becoming negative at the short end of the curve and distill the JGBs term structure of interest rate quite well. The affine-based extended model leads to a better in-sample fit than the simple GDNS model. In terms of out-of-sample accuracy, both non-affine models outperform the affine models at least for 1- and 6-month horizons. The out-of-sample predictability of the GDNS for the 1- and 6-month-ahead forecasts is superior to the GAFNS for all maturities, and for longer horizons, i.e., 12-month-ahead, the former is still compatible to the latter, particularly for short- and medium-term maturities.

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