Yield curve forecasting is an important problem in finance. In this work we explore the use of Gaussian Processes in conjunction with a dynamic modeling strategy, much like the Kalman Filter, to model the yield curve. Gaussian Processes have been successfully applied to model functional data in a variety of applications. A Gaussian Process is used to model the yield curve. The hyper-parameters of the Gaussian Process model are updated as the algorithm receives yield curve data. Yield curve data is typically available as a time series with a frequency of one day. We compare existing methods to forecast the yield curve with the proposed method. The results of this study showed that while a competing method (a multivariate time series method) performed well in forecasting the yields at the short term structure region of the yield curve, Gaussian Processes perform well in the medium and long term structure regions of the yield curve. Accuracy in the long term structure region of the yield curve has important practical implications. The Gaussian Process framework yields uncertainty and probability estimates directly in contrast to other competing methods. Analysts are frequently interested in this information. In this study the proposed method has been applied to yield curve forecasting, however it can be applied to model high frequency time series data or data streams in other domains.