A0160
Title: Prediction of functional moving average models
Authors: Johannes Klepsch - Technical University Munich (Germany) [presenting]
Claudia Klueppelberg - Technical University of Munich (Germany)
Abstract: First, a fully functional representation is given for the linear one-step predictor of the functional moving average (FMA) model in terms of the past of the process. Assuming invertibility of the process, we derive asymptotic properties of the operators involved in the representations of the predictors. Then, as the infinite dimensionality of the model prevents us from applying for example the innovation algorithm to compute the predictors, we project the FMA model on an arbitrary $K$-dimensional subspace. In contrast to the functional autoregressive model, we show that the projected FMA model still follows the dynamics of a FMA model of the same order or less, with a new K-dimensional innovation process. We show that we get arbitrarily close to the original FMA model by increasing $K$ and give implications for the prediction of FMA models.
