CRoNoS & MDA 2019: Start Registration
View Submission - CRONOSMDA2019
A0275
Title: Sparsely observed functional time series: Estimation and prediction 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 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. The subject is to tackle the problem of estimating the dynamics and of recovering the latent process of smooth curves in this sparse observation regime. We construct a consistent nonparametric estimator of the series' spectral density operator and use it develop a frequency-domain recovery approach, that predicts the latent curves at a given time by borrowing strength from the (estimated) dynamic correlations in the series across time. Further to predicting the latent curves from their noisy point samples, the method fills in gaps in the sequence (curves nowhere sampled), denoises the data, and serves as a basis for forecasting. Means of providing corresponding confidence bands are also investigated. The methodology is further illustrated by application to an environmental data set on fair-weather atmospheric electricity, which naturally leads to a sparse functional time-series.