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On residual empirical processes of GARCH‐SM models: application to conditional symmetry tests
Author(s) -
Laïb Naâmane,
Lemdani Mohamed,
OuldSaïd Elias
Publication year - 2008
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.1467-9892.2008.00580.x
Subject(s) - autoregressive conditional heteroskedasticity , mathematics , heteroscedasticity , residual , autoregressive model , asymptotic distribution , consistency (knowledge bases) , econometrics , statistic , studentized residual , test statistic , volatility (finance) , statistics , statistical hypothesis testing , estimator , algorithm , geometry
. Considering the generalized autoregressive conditionally heteroskedastic with stochastic mean (GARCH‐SM) model, we establish in this article the consistency and the weak representation of a functional of its residual empirical process. Based on this result, a symmetry test for GARCH‐SM model is developed. Simulations are given to show the asymptotic behaviour and normality of the test statistic.