Title: A functional dependence measure for large curve time series with an application to autoregressions
Authors: Xinghao Qiao - London School of Economics (United Kingdom) [presenting]
Shaojun Guo - Institute of Statistics and Big Data, Renmin Unversity of China (China)
Abstract: Modelling a large bundle of curves arises in a broad spectrum of real applications. However, many studies in functional data analysis literature focus primarily on the critical assumption of independent and identically distributed samples of a fixed number of curves. We introduce a measure of functional dependence for stationary functional processes that provides insights into the effect of cross-dependence among high dimensional curve time series. Based on our proposed functional dependence measure, we establish some useful concentration bounds for the relevant estimated terms when each component of the vector of curve time series is represented through its Karhunen-Lo\`eve expansion. As an example to illustrate, we propose vector functional autoregressive models, which characterize the dynamic dependence across high dimensional curve time series, and develop a regularization approach to estimate autoregressive coefficient functions. We then apply our developed concentration bound results to derive the non-asymptotic upper bounds for the estimation errors of the regularized estimates. We also show that the proposed method significantly outperforms its potential competitors through a series of simulated experiments and one real world data example. Finally, we discuss the application of our proposed functional dependence measure on some possible topics, e.g. causality and factor models.