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2015 Simultaneous inference of the mean of functional time series
Ming Chen, Qiongxia Song
Electron. J. Statist. 9(2): 1779-1798 (2015). DOI: 10.1214/15-EJS1052


For functional time series with physical dependence, we construct confidence bands for its mean function. The physical dependence is a general dependence framework, and it slightly relaxes the conditions of m-approximable dependence. We estimate functional time series mean functions via a spline smoothing technique. Confidence bands have been constructed based on a long-run variance and a strong approximation theorem, which is satisfied with mild regularity conditions. Simulation experiments provide strong evidence that corroborates the asymptotic theories. Additionally, an application to S&P500 index data demonstrates a non-constant volatility mean function at a certain significance level.


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Ming Chen. Qiongxia Song. "Simultaneous inference of the mean of functional time series." Electron. J. Statist. 9 (2) 1779 - 1798, 2015.


Received: 1 April 2015; Published: 2015
First available in Project Euclid: 25 August 2015

zbMATH: 1323.62031
MathSciNet: MR3391119
Digital Object Identifier: 10.1214/15-EJS1052

Primary: 62G08 , 62G15

Keywords: confidence bands , functional time series , high-frequency data , long-run variance , Nonparametric regression , Spline

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society


Vol.9 • No. 2 • 2015
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