Term Structure Forecasting: No-Arbitrage Restrictions versus Large Information Set

Abstract

This paper addresses the issue of forecasting term structure. We provide a unifi ed state-space modeling framework that encompasses different existing discrete-time yield curve models. Within such a framework we analyze the impact of two modeling choices, namely the imposition of no-arbitrage restrictions and the size of the information set used to extract factors, on forecasting performance. Using US yield curve data, we fi nd that both no-arbitrage and large information sets help in forecasting but no model uniformly dominates the other. No-arbitrage models are more useful at shorter horizons for shorter maturities. Large information sets are more useful at longer horizons and longer maturities. We also fi nd evidence for a signifi cant feedback from yield curve models to macroeconomic variables that could be exploited for macroeconomic forecasting.traditional fi nance literature limits the information set to a number of observable yields and uses two alternative methods: extraction of latent factors via cross-sectional interpolation methods and extraction of latent factors by exploiting no-arbitrage restrictions.Among the cross-sectional interpolation methods, the Nelson and Siegel (1987) approach is the most popular. The Nelson and Siegel three-factor model explains most variances of yields at different maturities with a very good in-sample fi t. Diebold and Li (2006) have successfully considered the out-of-sample forecasting performance of this model by assuming that the three factors follow AR(1) processes.Among no-arbitrage models, the common approach is to assume a linear model for the latent factors and to restrict the factor loadings so as to rule out arbitrage strategies on bonds of different maturities. No-arbitrage restrictions serve not only for reducing the dimension of the parameter space, but also contribute to the theoretical consistency of the model. Dai and Singleton (2000) and Piazzesi (2003) have surveyed the specifi cation issues of affi ne term structure models in continuous time and discrete time, respectively. Duffee (2002) has shown the usefulness of essentially affi ne term structure models (A 0 (3) 1 ) in forecasting.These two approaches have been recently merged in an affi ne arbitrage-free Nelson-Siegel (AFNS) model (see Christensen et al., 2007;Le Grand, 2007), where the traditional Nelson and Siegel structure is modifi ed to rule out arbitrage opportunities.Models mentioned above are traditionally based only on the information contained in the term structure. Financial markets are clearly not insulated from the rest of the economy. Feedback from the state of the economy to the short-term interest rate is explicitly considered in the monetary policy reaction function introduced by Taylor (1993) and by now widely adopted to explain the behavior of central banks.Several papers indicate that macroeconomic variables have strong effects on future movements of the yield curve (among others, Ang and Piazzesi, 2003;Rudebusch and Wu, 2008). In particular, Ang and Piazzesi (2003) use an A 0 ...

Predictions of short-term rates and the expectations hypothesis

“…We accomplish by implementing McCracken's (2004) nonparametric test for non-nested models, which takes into account the incremental variation in forecast errors due to parameter uncertainty. 29 We also use the more familiar Diebold and Mariano (1995) test.…”

“…where  is an average over  observations of the values taken by some differential loss function,   ≡ 28 The empirical rejection and poor forecasting performance of completely affine models is relatively unsurprising in the light of the literature (e.g., see Singleton, 2006). 29 When parameters are not known but must instead be estimated, West (1996) provides analytical tools that can be used to construct tests of equal forecast accuracy between non-nested models. His results are similar to those in Diebold and Mariano (1995) but require that the loss function used to measure forecast accuracy must be continuously differentiable.…”

Forecasting the Term Structure when Short‐Term Rates are Near Zero

“…While Duffee (2002) reports some success with a more flexible formulation of these models, the 'essentially affine' models, other authors have taken different approaches. Ang and Piazzesi (2003), Favero et al (2012) and Mönch (2008) applied no-arbitrage restrictions to VAR models, Diebold and Li (2006), de Pooter (2007) and Christensen et al (2009Christensen et al ( , 2011 examine dynamic versions (with and without no-arbitrage restrictions) of the Nelson-Siegel model of the cross section of yields, while Nyholm…”

The Sovereign Yield Curve and Fiscal Behaviour in China

“…As in previous studies (see e.g. Bernanke et al, 2005;Chen, 2009;Huse, 2011;Favero et al, 2012), besides the three latent factors, which are the level (L), the slope (S) and the curvature (C) of the yield curve, the present study also incorporates five macroeconomic variables and a fiscal variable (FB) in the VAR system.…”

“…Industrial production growth is a reasonable proxy for output growth (see e.g. Chen, 2009;Huse, 2011;Favero et al, 2012). Data for macroeconomic variables and fiscal variables are from WIND database.…”