Functional Autoregression for Sparsely Sampled 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 nonnegligible measurement error. The latent process is dyna...

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Bibliographic Details
Published in:Journal of business & economic statistics Vol. 37; no. 1; pp. 97 - 109
Main Authors: Kowal, Daniel R., Matteson, David S., Ruppert, David
Format: Journal Article
Language:English
Published: Alexandria Taylor & Francis 01.01.2019
American Statistical Association
Taylor & Francis Ltd
Subjects:
Functional factor analysis
Gaussian process
Hierarchical Bayes
Model averaging
Regression analysis
Time series
ISSN:0735-0015, 1537-2707
Online Access:Get full text
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Summary: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 nonnegligible 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. Real yields are observed more sparsely than nominal yields, yet the proposed methods are highly competitive in both settings. Supplementary materials, including R code and the yield curve data, are available online.
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ISSN:0735-0015
1537-2707
DOI:10.1080/07350015.2017.1279058