Our model and theory are developed in a general Hilbert space setting that allows for mixed panels of functional and scalar time series.
In Part I, we establish a representation result stating that, under mild assumptions on the covariance operator of the cross‐section, we can represent each FTS as the sum of a common component driven by scalar factors loaded via functional loadings, and a mildly cross‐correlated idiosyncratic component. In this paper, which consists of two parts (Part I: representation results Part II: estimation and forecasting methods), we set up the theoretical foundations for a high‐dimensional functional factor model approach in the analysis of large cross‐sections (panels) of functional time series (FTS).
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