Obviously a perfect forecast for interest rates is a bit hard to come by, such a thing would make the inventor quite a tidy sum. Broadly, the task you're seeking to accomplish falls under the banner of yield curve modeling, and there is a very substantial body of research in this area, including several good books.
There are some canonical examples of interest rate models, which mostly leverage the apparently mean reverting behavior of interest rate markets to construct a yield curve. One such model is the Diebold-Li model, an implementation of which is described at this link. This model is a four parameter forecasting tool for various interest rate regimes which takes into account the mean reverting behavior inherent in interest rates (they are generally believed to follow a ornstein uhlenbeck mean reverting stochastic process).
Another alternative is to calculate expectations implied by various maturity bonds. This can be done using various semi/non parametric smoothing methods. For this, you can use all of the estimators involved in non-linear regression. To my knowledge, no one technique has been proven superior.
Ultimately, this is an estimation problem. It isn't like option pricing where there is a single correct answer given a baseline set of regularity conditions.