Prediction of functional ARMA processes with an application to traffic data

For a functional ARMA(p, q) process an approximating vector model, based on functional PCA, is presented. Sufficient conditions are given for the existence of a stationary solution to both the functional and the vector model equations, and the structure of the approximating vector model is investigated. The stationary vector process is used to predict the functional process, where bounds for the difference between vector and functional best linear predictor are given. Finally, functional ARMA processes are applied for the modeling and prediction of highway traffic data.