Prediction of functional ARMA processes with an application to traffic data

Abstract: This work is devoted to functional ARMA$(p, q)$ processes and approximating vector models based on functional PCA in the context of prediction. After deriving sufficient conditions for the existence of a stationary solution to both the functional and the vector model equations, the structure of the approximating vector model is investigated. The stationary vector process is used to predict the functional process. A bound for the difference between vector and functional best linear predictor is derived. The paper concludes by applying functional ARMA processes for the modeling and prediction of highway traffic data.