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On the Distributional Properties of GARCH Processes
Author(s) -
Pawlak M.,
Schmid W.
Publication year - 2001
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00227
Subject(s) - autoregressive conditional heteroskedasticity , mathematics , econometrics , heteroscedasticity , autoregressive model , series (stratigraphy) , class (philosophy) , statistics , volatility (finance) , computer science , artificial intelligence , paleontology , biology
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.