Convolutional Functional Autoregressive Models: Model Building, Asymptotics, and Empirical Results

• Activity Number: 201
• Type: Contributed
• Date/Time: Monday, August 1, 2016 : 10:30 AM to 11:15 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Xialu Liu*
• Companies: San Diego State University
• Keywords: Functional time series ; Nonparametrics ; Spline methods ; Implied volatility ; Sieve estimation

Abstract

Functional data with serial dependence has received much attention over the last few decades. Bosq proposed FAR models in 2000. However, it is less complete due to lack of specific model assumptions. We propose a Convolutional Functional Autoregressive Model, along with its associated estimation procedure using splines and sieve methods. The asymptotics of our estimator is established, and model building procedure is developed. Our method is applied to implied volatility curves of S &P 500 index. It turns out that CFAR models outperform FAR models, and our method beats FPCA when predicting volatility curves.