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ON THE CORRELATION STRUCTURE FOR THE GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTIC PROCESS
Author(s) -
Bollerslev Tim
Publication year - 1988
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/j.1467-9892.1988.tb00459.x
Subject(s) - autoregressive conditional heteroskedasticity , heteroscedasticity , autoregressive model , mathematics , econometrics , series (stratigraphy) , correlation , star model , volatility (finance) , time series , statistics , autoregressive integrated moving average , paleontology , geometry , biology
. The correlation structure for the squares from the generalized autoregressive conditional heteroskedastic (GARCH) process is presented. It is shown that the behaviour of the correlations for the squares mimics the usual correlations of an appropriately defined ARMA process, although the admissible regions for the correlations are somewhat more restrictive. Simulation experiments are used to study the applicability of the theoretical results for order identification and diagnostic checking. Finally, an empirical example is given for the IBM stock market price series from Box and Jenkins (1976).