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Title: Sparsely observed functional time series: Estimation and regression Authors:  Tomas Rubin - EPFL (Switzerland) [presenting]
Victor Panaretos - EPFL (Switzerland)
Abstract: Functional time series analysis has traditionally been carried out under the assumption of complete observation of the constituent series of curves, assumed stationary. Nevertheless, it may very well happen that the data available to the analyst are not the actual sequence of curves, but relatively few and noisy measurements per curve, potentially at different locations in each curve's domain. First, we construct the spectral-domain-based estimator of the latent functional time series dynamics from noisy samples. Second, the estimated dynamic correlations are used to predict latent curves by borrowing strength across time. And third, we extend the framework to the lagged regression model where one functional time series is regressed onto another and show how to perform estimation and prediction from sparse and noisy data. The methodology is illustrated by application to financial data set on the US Treasury yield curve, a sparsely observed functional time series, being regressed on a time series of macroeconomic variables.