Monitoring shifts in mean: Asymptotic normality of stopping times

• Autores: Alexander Aue, Lajos Horváth, Piotr Kokoszka, Josef G. Steinebach
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 17, Nº. 3, 2008, págs. 515-530
• Idioma: inglés
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• Resumen

  • We consider a sequential procedure designed to detect a possible change in the mean of a random sequence. The procedure is motivated by the problem of detecting an early change in the mean of returns and is based on the CUSUM (cumulative sum) statistic. It terminates when the CUSUM crosses a boundary function or the number of collected observations reaches a prescribed number. We show that the stopping time is asymptotically normal. Simulations using models derived from returns on indexes and individual stocks show that the normal approximation holds in finite samples.