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Activity Number: 570 - New Frontiers of Functional Data Analysis
Type: Topic Contributed
Date/Time: Wednesday, August 1, 2018 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #329831
Title: A Functional Dependence Measure for Large Curve Time Series with an Application to Autoregressions
Author(s): Xinghao Qiao* and Shaojun Guo
Companies: LSE and Renmin University of China
Keywords: Functional data; Time Series; Concentration inequality; High dimensionality; Karhunen-Loeve expansion; Autoregression
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 iid 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 estimates when each component of the vector of curve time series is represented through its Karhunen-Loeve 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 inequalities 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 both simulations and one real data example.


Authors who are presenting talks have a * after their name.

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