Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 9, Number 2 (2015), 1779-1798.
Simultaneous inference of the mean of functional time series
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.
Electron. J. Statist., Volume 9, Number 2 (2015), 1779-1798.
Received: April 2015
First available in Project Euclid: 25 August 2015
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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