Starting from the work by Campbell and Shiller (Campbell, J.Y. and Shiller, R.J. (1987). Cointegration and tests of present value models. Journal of Political Economy, 95(5):1062–1088.), empirical analysis of interest rates has been conducted in the framework of cointegration. However, parts of this approach have been questioned recently, as the adjustment mechanism may not follow a simple linear rule; another line of criticism points out that stationarity of the spreads is difficult to maintain empirically. In this paper, we analyse data on US bond yields by means of an augmented VAR specification which approximates a generic nonlinear adjustment model. We argue that nonlinearity captures macro information via the shape of the yield curve and thus provides an alternative explanation for some findings that recently appeared in the literature. Moreover, we show how conditional heteroskedasticity can be taken into account via GARCH specifications for the conditional variance, either univariate or multivariate.