A bootstrap test for additive outliers in non-stationary time series
Article first published online: 28 MAY 2013
© 2013 Wiley Publishing Ltd.
Journal of Time Series Analysis
Volume 34, Issue 4, pages 454–465, July 2013
How to Cite
Astill, S., Harvey, D. I. and Robert Taylor, A. M. (2013), A bootstrap test for additive outliers in non-stationary time series. Journal of Time Series Analysis, 34: 454–465. doi: 10.1111/jtsa.12033
- Issue published online: 18 JUN 2013
- Article first published online: 28 MAY 2013
- Manuscript Received: 15 JUN 2012
- Additive outliers;
In this paper we propose a new procedure for detecting additive outliers in a univariate time series based on a bootstrap implementation of the test of Perron and Rodríguez (2003, Journal of Time Series Analysis 24, 193-220). This procedure is used to test the null hypothesis that a time series is uncontaminated by additive outliers against the alternative that one or more additive outliers are present. We demonstrate that the existing tests of, inter alia, Vogelsang (1999, Journal of Time Series Analysis 20, 237–52) Perron and Rodríguez (2003) and Burridge and Taylor (2006, Journal of Time Series Analysis 27, 685–701) are unable to strike a balance between size and power when the order of integration of a time series is unknown and the time series is driven by innovations drawn from an unknown distribution. We show that the proposed bootstrap testing procedure is able to control size to such an extent that its size properties are comparable with the robust test of Burridge and Taylor (2006) when the distribution of the innovations is not assumed known, whilst maintaining power in the Gaussian environment close to that of the test of Perron and Rodríguez (2003).