Electronic Journal of Statistics

Simultaneous inference of the mean of functional time series

Ming Chen and Qiongxia Song

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Statist., Volume 9, Number 2 (2015), 1779-1798.

Dates
Received: April 2015
First available in Project Euclid: 25 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1440507393

Digital Object Identifier
doi:10.1214/15-EJS1052

Mathematical Reviews number (MathSciNet)
MR3391119

Zentralblatt MATH identifier
1323.62031

Subjects
Primary: 62G08: Nonparametric regression 62G15: Tolerance and confidence regions

Keywords
Confidence bands functional time series high-frequency data long-run variance nonparametric regression spline

Citation

Chen, Ming; Song, Qiongxia. Simultaneous inference of the mean of functional time series. Electron. J. Statist. 9 (2015), no. 2, 1779--1798. doi:10.1214/15-EJS1052. https://projecteuclid.org/euclid.ejs/1440507393


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