Electronic Journal of Statistics

Testing for jumps in the presence of smooth changes in trends of nonstationary time series

Ting Zhang

Full-text: Open access

Abstract

Nonparametric smoothing methods have been widely used in trend analysis. However, the inference procedure usually requires the crucial assumption that the underlying trend function is smooth. This paper considers the situation where the trend function has potential jumps in addition to smooth changes. In order to determine the existence of jumps, we propose a nonparametric test that can survive under dependent and nonstationary errors, where existing tests assuming independence or stationarity can fail. When the existence of jumps is affirmative, we further consider the problem of estimating the number, location and size of jumps. The results are illustrated via both Monte Carlo simulations and a real data example.

Article information

Source
Electron. J. Statist., Volume 10, Number 1 (2016), 706-735.

Dates
Received: August 2015
First available in Project Euclid: 18 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1458323995

Digital Object Identifier
doi:10.1214/16-EJS1127

Mathematical Reviews number (MathSciNet)
MR3477739

Zentralblatt MATH identifier
06561111

Keywords
Abrupt and smooth changes change points local linear estimation nonparametric hypothesis testing nonparametric jump detection nonstationary processes

Citation

Zhang, Ting. Testing for jumps in the presence of smooth changes in trends of nonstationary time series. Electron. J. Statist. 10 (2016), no. 1, 706--735. doi:10.1214/16-EJS1127. https://projecteuclid.org/euclid.ejs/1458323995


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