Cusum of squares-based tests for a change in persistence

Stephen Leybourne, Robert Taylor, Tae Hwan Kim

Research output: Contribution to journalArticlepeer-review

56 Citations (Scopus)


Using standardized cumulative sums of squared sub-sample residuals, we propose a new ratio-based test of the null hypothesis that a time series exhibits no change in its persistence structure [specifically that it displays constant I(1) behaviour] against the alternative of a change in persistence from trend stationarity to difference stationarity, or vice versa. Neither the direction nor location of any possible change under the alternative hypothesis need be assumed known. A key feature of our proposed test which distinguishes it from extant tests for persistence change [certain of which test the null hypothesis of constant I(0) behaviour while others, like our proposed test, test the null hypothesis of constant 7(1) behaviour] is that it displays no tendency to spuriously overreject when applied to series which, although not constant I(1) series, do not display a change in persistence [specifically are constant I(0) processes]. Moreover, where our ratio test correctly rejects the null of no persistence change, the tail in which the rejection occurs can also be used to identify the direction of change since, even in relatively small samples, the test almost never rejects in the right [left] tail when there is a change from I(0) to I(1) [I(1) to I(0)]. Again this useful property is not shared by existing tests. As a by-product of our analysis, we also propose breakpoint estimators which are consistent where the timing of the change in persistence is unknown.

Original languageEnglish
Pages (from-to)408-433
Number of pages26
JournalJournal of Time Series Analysis
Issue number3
Publication statusPublished - 2007 May

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


Dive into the research topics of 'Cusum of squares-based tests for a change in persistence'. Together they form a unique fingerprint.

Cite this