Usually forecasting is based on a model for the evolution of a value $x(t)$ based on some parameters ${\beta}$ that can then be estimated using various statistical means.
For yield curves and volatilities however, we do not have a single point $x(t)$ but a range of points $\{x_1(t), ..., x_n(t)\}$ that all need to be forecasted at once and in a way that preserves some inherent structure in the data.
What are the state-of-the-art methods to do so for rates and volatilities?
