Asymptotic theory for QMLE for the real‐time GARCH(1, 1) model. (6th January 2021)

• Record Type: Journal Article
• Authors: Smetanina, Ekaterina; Biao Wu, Wei
• Other Names: Bradley Richard C. guestEditor.; Davis Richard A. guestEditor.; Politis Dimitris N. guestEditor.
• Is Part Of: Journal of time series analysis. Volume 42:Number 5/6(2021)
• Page Start: 752
• Page End: 776
• Publication Date: 2021-01-06
• Subjects: GARCH -- stationarity -- asymptotic theory -- derivative processes; Time-series analysis -- Periodicals; 519.232
• DOI: 10.1111/jtsa.12578
• Languages: English
• ISSNs: 0143-9782

Abstract

Abstract : We investigate the asymptotic properties of the Gaussian quasi‐maximum‐likelihood estimator (QMLE) for the Real‐time GARCH(1, 1) model of Smetanina (2017, Journal of Financial Econometrics, 15(4), 561–601). The developed theory relies on the functional dependence measure and recently developed theory for derivative processes in Dahlhaus etal. (2019, Bernoulli, 25(2), 1013–1044). We prove stationarity and ergodicity of the underlying processes and consistency for the QMLE estimator under mild conditions. Furthermore, under normality of the error term, we also establish asymptotic normality for QMLE, which then becomes MLE, at the usual T rate. Finally, in our simulations we show that consistency and asymptotic normality holds for typical sample sizes.