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Activity Number: 35 - Special Session: Section on Nonparametric Statistics Student Paper Competition
Type: Contributed
Date/Time: Sunday, July 30, 2017 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #322647 View Presentation
Title: Functional Autoregression for Sparsely Sampled Data
Author(s): Daniel Kowal* and David S Matteson and David Ruppert
Companies: Cornell University and Cornell University and Cornell University
Keywords: functional factor analysis ; Gaussian process ; hierarchical Bayes ; Model averaging ; time series ; functional data

We develop a hierarchical Gaussian process model for forecasting and inference of functional time series data. Unlike existing methods, our approach is especially suited for sparsely or irregularly sampled curves and for curves sampled with non-negligible measurement error. The latent process is dynamically modeled as a functional autoregression (FAR) with Gaussian process innovations. We propose a fully nonparametric dynamic functional factor model for the dynamic innovation process, with broader applicability and improved computational efficiency over standard Gaussian process models. We prove finite-sample forecasting and interpolation optimality properties of the proposed model, which remain valid with the Gaussian assumption relaxed. An efficient Gibbs sampling algorithm is developed for estimation, inference, and forecasting, with extensions for FAR(p) models with model averaging over the lag p. Extensive simulations demonstrate substantial improvements in forecasting performance and recovery of the autoregressive surface over competing methods, especially under sparse designs. We apply the proposed methods to forecast nominal and real yield curves using daily U.S. data.

Authors who are presenting talks have a * after their name.

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