Functional Autoregression for Sparsely Sampled Data

Abstract

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. Real yields are observed more sparsely than nominal yields, yet the proposed methods are highly competitive in both settings.

References in corpus (1)

• Functional dynamic factor models with application to yield curve forecasting

Cited by in corpus (12)

• Learning Long-Term Dependencies in Irregularly-Sampled Time Series
• Robust multivariate and functional archetypal analysis with application to financial time series analysis
• Sparsely Observed Functional Time Series: Estimation and Prediction
• Modern Multiple Imputation with Functional Data
• Highly Irregular Functional Generalized Linear Regression with Electronic Health Records
• Functional Lagged Regression with Sparse Noisy Observations
• Dynamic Function-on-Scalars Regression
• Bayesian Testing Of Granger Causality In Functional Time Series
• A Uniform Bound on the Operator Norm of Sub-Gaussian Random Matrices and Its Applications
• Yield curve and macroeconomy interaction: evidence from the non-parametric functional lagged regression approach
• Semiparametric Functional Factor Models with Bayesian Rank Selection
• Uncovering predictability in the evolution of the WTI oil futures curve