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On residual empirical processes of GARCH‐SM models: application to conditional symmetry tests |
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| Authors: | Naâmane Laïb Mohamed Lemdani Elias Ould‐Saïd |
| Affiliation: | 1. Univ. Paris 6;2. Univ. de Lille 2;3. Univ. du Littoral C?te d'Opale |
| Abstract: | Abstract. 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. |
| Keywords: | AR‐GARCH model asymptotic normality consistency goodness‐of‐fit residual law symmetry test weak representation 62M10 62G10 |