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Title: Estimation of functional ARMA models Authors:  Thomas Kuenzer - Medical University of Graz (Austria) [presenting]
Abstract: Functional auto-regressive moving average (FARMA or ARMAH) models allow for flexible and natural modelling of functional time series. While there are many results on pure autoregressive (FAR) models in Hilbert spaces, results on estimation and prediction of FARMA models are considerably more scarce. We devise a simple two-step method to estimate ARMA models in separable Hilbert spaces. Estimation is based on dimension-reduction using principal components analysis of the functional time series. We establish consistency of the proposed estimators under simple assumptions by employing a data-driven criterion to select the dimensionality of the principal component subspaces used in the estimation procedure. The empirical performance of the estimation algorithm is evaluated in a simulation study, where it performs better than competing methods.