Interest Rates with Long Memory: A Generalized Affine Term-Structure Model

We propose a model for the term structure of interest rates that is a generalization of the discrete-time, Gaussian, affine yield-curve model. Compared to standard affine models, our model allows for general linear dynamics in the vector of state variables. In an application to real yields of U.S. government bonds, we model the time series of the state vector by means of a co-fractional vector autoregressive model. The implication is that yields of all maturities exhibit nonstationary, yet mean-reverting, long-memory behavior of the order d ˜ 0.87. The long-run dynamics of the state vector are driven by a level, a slope, and a curvature factor that arise naturally from the co-fractional modeling framework. We show that implied yields match the level and the variability of yields well over time. Studying the out-of-sample forecasting accuracy of our model, we find that our model results in good yield forecasts that outperform several benchmark models, especially at long forecasting horizons.