Detection of a changepoint, a mean-shift accompanied with a trend change, in short time-series with autocorrelation

ABSTRACT

In this study, a changepoint model, which can detect either a mean shift or a trend change when accounting for autocorrelation in short time-series, was investigated with simulations and a new method is proposed. The changepoint hypotheses were tested using a likelihood ratio test. The test statistic does not follow a known distribution and depends on the length of the time-series and the autocorrelation. The results imply that it is not possible to detect autocorrelation and that the estimate of the autocorrelation parameter is biased. It is therefore recommended to use critical values from the empirical distribution for a fixed autocorrelation.

KEYWORDS:

• Autocorrelation
• Changepoint
• Likelihood ratio test
• Time-series

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62M10
• Secondary 62F03, 62H10, 62Q05

Acknowledgments

This study was funded by the Icelandic Research Fund and the Icelandic Research Fund for Graduate Students.