# In this paper we assess the extent

In this paper we assess the extent to which the imposition of a no-arbitrage restriction on the DNS setting brings additional forecasting gains by providing an empirical evidence based on a large data set of constant-maturity future contracts of the Brazilian Inter Bank Deposit Contract (DI1) which is equivalent to a zero-coupon bond and is highly liquid (293million contracts worth US$ 15billion traded in 2010). The market for DI1 contracts is one of the most liquid interest rate markets in the world. Many banks, insurance companies, and investors use DI1 contracts as investment and hedging instruments. The data set considered in the paper contains daily observations of DI1 contracts traded on the Brazilian Mercantile and Futures Exchange (BM&F) with fixed maturities of 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 42, and 48 months. We use a rolling estimation to produce out-of-sample forecasts for 1-week, 1-month, 3-month, and 6-month ahead based on the DNS and AFNS models with both uncorrelated and correlated factors. Moreover, we consider three alternative classical benchmark specifications: the random walk (RW) model, which is taken as our baseline model, the unrestricted first-order autoregressive model (AR(1)), and the first-order vector-autoregressive model (VAR(1)). We assess forecasting accuracy of a model for each of the 14 maturities by means of the root mean squared forecast error (RMSFE), and the overall performance of a given model by the trace RMSFE (TRMSFE) considered in Hoerdahl et al. (2006), de Pooter et al. (2010). Finally, we also test for the differences in forecasting performance using the test proposed in Giacomini and White (2006).
Our empirical evidence suggests that when a short forecasting horizon is considered (e.g. 1-week-ahead), the differences in forecasting performance among the candidate models is rather inconclusive since in very few instances the baseline RW model is outperformed. However, it cyp450 inducers is possible to see that when longer forecasting horizons are considered, the AFNS model with uncorrelated factors appears to deliver the most accurate forecasts. Therefore, the most important message from our empirical test is that the imposition of no-arbitrage is indeed helpful, but only for longer (e.g. 3-month- and 6-month-ahead) forecasting horizons. These results corroborate the evidence reported in Christensen et al. (2011) for US Treasuries data, as they find that the AFNS model with independent factors outperforms the DNS specifications for the 6-month- and 12-month-ahead forecast horizons. Our results corroborate the findings in Araújo and Cajueiro (2013), Caldeira et al. (2016), who shows that trisomy is not possible to determine an individual model that consistently produces superior forecasts for all maturities and all forecasts horizons. Nevertheless, empirical results suggest that the traditional DNS model has good out-of-sample forecasting performance when compared to the RW, AR(1), and VAR(1), specially when we consider 1- and 3-month ahead horizon.
The outline of the paper is as follows. Section 2 describes the DNS and AFNS specifications adopted in this paper. Section 3 discusses the implementation details and empirical results. Finally, Section 4 concludes.

The Nelson–Siegel class of models
Nelson and Siegel (1987) have shown that the term structure can be surprisingly well fitted at a particular point in time by a linear combination of three smooth functions. The Nelson–Siegel model of the yield curve is given bywhere y(τ) is the zero-coupon yield with τ months to maturity, and β1, β2, and β3 can be interpreted as the level, slope, and curvature of the yield curve, respectively. The parameter λ determines the exponential decay of the β2 and β3 loadings.

Empirical analysis

Concluding remarks
The dynamic version of the Nelson–Siegel model has been shown in the literature to be remarkably well suited both to fit and to forecast the term structure of interest rates. More recently, Christensen et al. (2011) have developed an arbitrage-free version of this model in order to bring theoretical rigor to a empirically successful model. In this paper, we have analyzed the forecasting power of no-arbitrage restrictions on the dynamic Nelson–Siegel model in order to determine the empirical relevance of this new theoretical restriction.