Modelling the term structure of Japanese bond yields with the Nelson-Siegel model

Abstract

The Nelson-Siegel (1987) (NS) model has been credited for its high efficacy in the in-sample fitting and out-of-sample forecasting of the term structures of interest rates. The term structure of interest rates, popularly known as the yield curve, is a static function that relates the time-to-maturity to the yield-tomaturity for a sample of bonds at a given point in time. The conventional way of measuring the term structure is by means of the spot rate curve, or yield curve, on zero-coupon bonds. Yet in reality, the entire term structure is not directly observable, which gives rise to the need to estimate it using several approximation techniques. Over the last three decades, various methods to estimate term structures from bond prices have been proposed. In recent years most of the existing studies (as well as major central banks around the globe) have been employing the class of NS models to estimate and construct zero-coupon yield curves. This paper aims to study the term structure of the Japanese bond yields by employing the NS model vs other non-NS models using five different sets of zero-coupon bond yield rates data obtained from the Bank of Japan covering the period spanning from January 2000 to November 2007. This period has been chosen because it clearly exhibits the liquidity trap problem, which forces all bond yields to remain close to zero for an extended period. We propose 18 different NS models, each with different decay components and time series appendages, against 14 other non-NS models ranging from the simple random-walk model to complicated specifications like the VAR and VECM models. A h-period(s)-ahead out-of-sample expanding window forecast is conducted for each of these 32 different models, using daily, weekly and monthly bond yields of 15 different maturities. This study has demonstrated that due to the presence of liquidity trap in Japan, out-of-sample expanding window forecasts in general perform inferiorly vis-à-vis other non-NS models, and this is coupled with the other problem of obtaining negative yield forecasts for bonds with shorter maturities. Moreover, the results show that the NS class of models can be useful in forecasting shorter horizons like weeks and days, works better with a decay rate other than the conventional way of treating it as the value that maximizes the loading on the medium-term factor at exactly 30 months, and can work well with time series models such as GARCH and EGARCH in terms of volatility forecasting. It is also found that, when the NS models are used for yield forecasts, the NS-VAR model should be considered since it is up to par against the competitor models, even with liquidity trap at work.