## A multiple window scan statistic for time series models.(English)Zbl 1333.62052

Summary: In this article we extend the results derived for scan statistics in [X. Wang and J. Glaz, Commun. Stat., Theory Methods 43, No. 10–12, 2489–2504 (2014; Zbl 1314.62062)] for independent normal observations. We investigate the performance of two approximations for the distribution of fixed window scan statistics for time series models. An $$R$$ algorithm for computing multivariate normal probabilities established in [A. Genz and F. Bretz, Computation of multivariate normal and $$t$$ probabilities. Berlin: Springer (2009; Zbl 1204.62088)] can be used along with proposed approximations to implement fixed window scan statistics for ARMA models. The accuracy of these approximations is investigated via simulation. Moreover, a multiple window scan statistic is defined for detecting a local change in the mean of a Gaussian white noise component in ARMA models, when the appropriate length of the scanning window is unknown. Based on the numerical results, for power comparisons of the scan statistics, we can conclude that when the window size of a local change is unknown, the multiple window scan statistic outperforms the fixed window scan statistics.

### MSC:

 62E17 Approximations to statistical distributions (nonasymptotic) 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)

### Citations:

Zbl 1314.62062; Zbl 1204.62088

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### References:

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