, Volume 21, Issue 4, pp 605–634 | Cite as

Monitoring changes in the error distribution of autoregressive models based on Fourier methods

  • Zdeněk Hlávka
  • Marie Hušková
  • Claudia Kirch
  • Simos G. MeintanisEmail author
Original Paper


We develop a procedure for monitoring changes in the error distribution of autoregressive time series while controlling the overall size of the sequential test. The proposed procedure, unlike standard procedures which are also referred to, utilizes the empirical characteristic function of properly estimated residuals. The limit behavior of the test statistic is investigated under the null hypothesis as well as under alternatives. Since the asymptotic null distribution contains unknown parameters, a bootstrap procedure is proposed in order to actually perform the test and corresponding results on the finite–sample performance of the new method are presented. As it turns out the procedure is not only able to detect distributional changes but also changes in the regression coefficient.


Empirical characteristic function Change point analysis 

Mathematics Subject Classification (2000)

62M10 62G10 62G20 


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2011

Authors and Affiliations

  • Zdeněk Hlávka
    • 1
  • Marie Hušková
    • 1
  • Claudia Kirch
    • 2
  • Simos G. Meintanis
    • 3
    Email author
  1. 1.Faculty of Mathematics and Physics, Department of StatisticsCharles University in PraguePraha 8Czech Republic
  2. 2.Institute of StochasticsKarlsruhe Institute of TechnologyKarlsruheGermany
  3. 3.Department of EconomicsNational and Kapodistrian University of AthensAthensGreece

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