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The ARL of modified Shewhart control charts for conditionally heteroskedastic models

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  • Esmeralda Gonçalves
  • Joana Leite
  • Nazaré Mendes-Lopes

Abstract

In this article we consider the modified Shewhart control chart for ARCH processes and introduce it for threshold ARCH (TARCH) ones. For both charts, we determine bounds for the distribution of the in-control run length (RL) and, consequently, for its average (ARL), both depending only on the distribution of the generating white noise, the model parameters and the critical value. For the ARCH model, we compare our bounds with others available in literature and show how they improve the existing ones. We present a simulation study to assess the quality of the bounds calculated for the ARL. Copyright Springer-Verlag 2013

Suggested Citation

  • Esmeralda Gonçalves & Joana Leite & Nazaré Mendes-Lopes, 2013. "The ARL of modified Shewhart control charts for conditionally heteroskedastic models," Statistical Papers, Springer, vol. 54(1), pages 1-19, February.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:1:p:1-19
    DOI: 10.1007/s00362-011-0408-z
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    References listed on IDEAS

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    1. M. Pawlak & W. Schmid, 2001. "On the Distributional Properties of GARCH Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(3), pages 339-352, May.
    2. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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