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Epidemic change tests for the mean of innovations of an AR(1) process

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  • Markevičiūtė, J.

Abstract

We study a first order autoregressive process with the autoregressive coefficient ϕ=1 or |ϕ|<1. Our aim is to test whether there is an epidemic type change in the mean of innovations with the statistics based on the observations. We use two equivalent Hölderian test statistics: uniform and dyadic increments statistics. We find the limit under null hypothesis of no change, then we establish consistency conditions under alternative.

Suggested Citation

  • Markevičiūtė, J., 2016. "Epidemic change tests for the mean of innovations of an AR(1) process," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 79-91.
    • Handle: RePEc:eee:stapro:v:112:y:2016:i:c:p:79-91
    DOI: 10.1016/j.spl.2016.02.001
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    References listed on IDEAS

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    1. Natalie Neumeyer & Ingrid Van Keilegom, 2009. "Change‐Point Tests for the Error Distribution in Non‐parametric Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 518-541, September.
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    5. Leonie Selk & Natalie Neumeyer, 2013. "Testing for a Change of the Innovation Distribution in Nonparametric Autoregression: The Sequential Empirical Process Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 770-788, December.
    6. Zdeněk Hlávka & Marie Hušková & Claudia Kirch & Simos Meintanis, 2012. "Monitoring changes in the error distribution of autoregressive models based on Fourier methods," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 605-634, December.
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