A Scale-space Approach for Detecting Non-stationarities in Time Series
Article first published online: 4 FEB 2008
© 2007 Board of the Foundation of the Scandinavian Journal of Statistics.
Scandinavian Journal of Statistics
Volume 35, Issue 1, pages 119–138, March 2008
How to Cite
OLSEN, L. R., SØRBYE, S. H. and GODTLIEBSEN, F. (2008), A Scale-space Approach for Detecting Non-stationarities in Time Series. Scandinavian Journal of Statistics, 35: 119–138. doi: 10.1111/j.1467-9469.2006.00556.x
- Issue published online: 4 FEB 2008
- Article first published online: 4 FEB 2008
- Received December 2005, in final from November 2006
- change point;
- quadratic forms;
- scale space;
- time series
Abstract. The presented method called Significant Non-stationarities, represents an exploratory tool for identifying significant changes in the mean, the variance, and the first-lag autocorrelation coefficient of a time series. The changes are detected on different time scales. The statistical inference for each scale is based on accurate approximation of the probability distribution, using test statistics being ratios of quadratic forms. No assumptions concerning the autocovariance function of the time series are made as the dependence structure is estimated non-parametrically. The results of the analyses are summarized in significance maps showing at which time points and on which time scales significant changes in the parameters occur. The performance of the given method is thoroughly studied by simulations in terms of observed significance level and power. Several examples, including a real temperature data set, are studied. The examples illustrate that it is important to carry out the analysis on several time horizons.