Simultaneous Inference for the Mean of Functional Time Series

• Activity Number: 90
• Type: Invited
• Date/Time: Sunday, August 9, 2015 : 8:30 PM to 9:15 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Ming Chen* and Qiongxia Song
• Companies: The University of Texas at Dallas and The University of Texas at Dallas
• Keywords: confidence bands ; functional time series ; high-frequency data ; long-run variance ; nonparametric regression ; spline

Abstract

For functional time series with physical dependence, we construct confidence bands for its mean function. The physical dependence is a general dependence frame, and it slightly relaxes the conditions of m- approximable dependence. We estimate functional time series mean functions via spline smoothing technique. Confidence bands have been constructed based on a long-run variance decomposition and a strong approximation, which are satisfied under mild regularity conditions. Simulation experiments provide strong evidence that corroborates the asymptotic theories. Additionally, an application to S&P 500 index data demonstrates a non-constant volatility mean function at a certain significance level.