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A Model Specification Test For GARCH(1,1) Processes
Author(s) -
Leucht Anne,
Kreiss JensPeter,
Neumann Michael H.
Publication year - 2015
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12158
Subject(s) - mathematics , autoregressive conditional heteroskedasticity , test statistic , heteroscedasticity , autoregressive model , asymptotic distribution , null distribution , econometrics , goodness of fit , statistic , statistics , statistical hypothesis testing , estimator , volatility (finance)
We provide a consistent specification test for generalized autoregressive conditional heteroscedastic (GARCH (1,1)) models based on a test statistic of Cramér‐von Mises type. Because the limit distribution of the test statistic under the null hypothesis depends on unknown quantities in a complicated manner, we propose a model‐based (semiparametric) bootstrap method to approximate critical values of the test and to verify its asymptotic validity. Finally, we illuminate the finite sample behaviour of the test by some simulations.