Convolutional Functional Autoregressive Models: Inference and Prediction

• Activity Number: 355
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Xialu Liu* and Han Xiao and Rong Chen
• Companies: Rutgers University and Rutgers University and Rutgers University
• Keywords: Functional time series ; Nonparametric methods ; Spline methods ; Sieve estimation

Abstract

Functional data analysis has became an increasingly popular class of problems in statistical research. However, functional data observed over time with serial dependence remains a less studied area. We propose a convolutional functional autoregressive model, where the function at time t is a result of the sum of convolutions of the past functions with a set of convolution functions, plus a noise process, mimicking the autoregressive process. It provides an intuitive and direct interpretation of the dynamics of a stochastic process. We establish convergence rate of the proposed estimator, and investigate its theoretical properties. The model building, model validation, and prediction procedures are also developed.