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On the Distributional Properties of GARCH Processes

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  • M. Pawlak
  • W. Schmid

Abstract

In this paper we study the distributional properties of the generalized autoregressive conditional heteroskedasticity (GARCH) model often being applied in economics. For a large class of non‐normal distributions of the noise process various inequalities on the distribution of the GARCH process are established. Moreover, these results are used to derive useful conclusions about the behavior of the average run length of a Shewhart control chart for time series.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:22:y:2001:i:3:p:339-352
    DOI: 10.1111/1467-9892.00227
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    Cited by:

    1. Schmid Wolfgang & Okhrin Yarema, 2003. "Tail behaviour of a general family of control charts," Statistics & Risk Modeling, De Gruyter, vol. 21(1/2003), pages 79-92, January.
    2. 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.
    3. Fernandes, Marcelo, 2004. "Bounds for the probability distribution function of the linear ACD process," Statistics & Probability Letters, Elsevier, vol. 68(2), pages 169-176, June.

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