Forecasting the Term Structure of South African Government Bond Yields

ABSTRACT

This article uses the parsimonious dynamic Nelson–Siegel model to fit the yields of South African government bonds. We find that the dynamic Nelson–Siegel model has good fitting abilities for all maturities. We further forecast the term structure by seven different dynamic Nelson–Siegel models with time series models. We find that the DNS–VAR–GARCH model is useful for forecasting the short-term rates, the DNS–VAR best predicts the medium-term rates, and the DNS–RW best predicts the long-term rates. In addition, the dynamic Nelson–Siegel models provide better forecasts of yield data than a random walk model, especially for the 12-month forecasting horizons.

KEY WORDS:

• dynamic Nelson–Siegel model
• forecasting
• South African government bond
• term structure

Notes

1. Theoretically speaking, a smaller value of ${\lambda }_t$ is supposed to produce slow decay and can thus better fit the yield curve at long maturities.

2. We use the augmented-Dickey–Fuller (ADF) tests to examine the stationary process of our data. We find that the yields and most estimated factors are nonstationary, but the first-difference variables become stationary at the 1% level. Next, we use Akaike’s information criterion (AIC) to determine the maximum lag length with the estimated factors for the Nelson–Siegel model. The results show that the optimal models are AR(1), ARMA(1,1), and VAR(1).

3. Duffee (2002) found that the forecast accuracy of the simplest random walk forecasts is better than the Dai and Singleton (2002) affine models. Diebold and Li (2006) compared the forecast accuracy of dynamic Nelson–Siegel models with the random walk model. The forecast by the random walk model (RW) is given by

${\hat{y}}_{t+h}\left(\tau \right)=y_t\left(\tau \right).$

where ${\hat{y}}_{t+h}\left(\tau \right)$ is the forecast of the yield, and h is the forecast horizon.