On the empirical characteristic function process of the residuals in GARCH models and applications
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[1] Universidad de Sevilla
Universidad de Sevilla
Sevilla, España
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- Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 23, Nº. 2, 2014, págs. 409-432
- Idioma: inglés
- DOI: 10.1007/s11749-014-0359-5
- Texto completo no disponible (Saber más ...)
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Resumen
The class of generalized autoregressive conditional heteroscedastic (GARCH) models has been proved to be particularly valuable in modeling financial data. This paper is devoted to study the empirical characteristic function process of the residuals. Specifically, it is shown that such process uniformly converges to the population characteristic function (CF) of the innovations in compact sets. The weak convergence of this empirical process, suitably normalized, is also studied. The limit depends on the population CF of the innovations, the equation defining the GARCH model and the parameter estimators employed to calculate the residuals. Applications of the obtained results for testing symmetry and goodness-of-fit to the law of the innovations are given.
