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Title: A dynamic factor model for functional time series: Identification, estimation, and prediction Authors:  Sven Otto - University of Bonn (Germany) [presenting]
Nazarii Salish - University Carlos III de Madrid (Spain)
Abstract: A fully functional factor model is proposed in which both the common component and the idiosyncratic component are random elements of the Hilbert space of L2 integrable functions on a bounded domain. We assume that the factors are dynamic and follow a vector autoregressive process, while the errors are H-white noise. Together with suitable conditions for the factors and loading functions, the common factor dynamics allows us to identify the factor and the error component separately. By applying the least-squares principle, we obtain an estimator based on functional principal components which are shown to be consistent. The number of factors and lags are jointly estimated by a forecast error based information criterion. For curve predictions, we suggest the minimum mean square error forecast from the dynamic functional factor model, and prediction bands are provided under additional distributional assumptions. Finally, the methodology is applied to the problem of yield curve modeling and forecasting. In an out-of-sample experiment, it is shown that the predictions can be significantly improved when compared to the predictor from the dynamic Nelson-Siegel model, which is the most commonly used term structure model for yield curves.