1. Decompose the smooth curves via a functional principal component analysis (FPCA).
2. Fit a multivariate time-series model to the principal component score matrix.
3. Forecast the principal component scores using the fitted multivariate time-series models. The order of VAR is selected optimally via an information criterion.
4. Multiply the forecast principal component scores by estimated principal components to obtain forecasts of \(f_{n+h}(x)\).
5. Prediction intervals are constructed by taking quantiles of the one-step-ahead forecast errors.