QIONGXIA SONG 
Department of Mathematical Sciences
University of Texas at Dallas
“Simultaneous Inference for the Mean of Functional Time Series”
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.
Keywords: confidence bands, functional time series, high-frequency data, long-run variance, nonparametric regression, spline.
Joint work with Ming Chen.
