Robust bootstrap forecast densities for GARCH returns and volatilities

ABSTRACT

Bootstrap procedures are useful to obtain forecast densities for both returns and volatilities in the context of generalized autoregressive conditional heteroscedasticity models. In this paper, we analyse the effect of additive outliers on the finite sample properties of these bootstrap densities and show that, when obtained using maximum likelihood estimates of the parameters and standard filters for the volatilities, they are badly affected with dramatic consequences on the estimation of Value-at-Risk. We propose constructing bootstrap densities for returns and volatilities using a robust parameter estimator based on variance targeting implemented together with an adequate modification of the volatility filter. We show that the performance of the proposed procedure is adequate when compared with available robust alternatives. The results are illustrated with both simulated and real data.

KEYWORDS:

• BM estimator
• outliers
• smooth bootstrap
• variance targeting
• Winsorized bootstrap

Acknowledgments

Part of this research was carried out during a visit of the first two authors to the Department of Statistics of the University Carlos III de Madrid whose hospitality is acknowledged. M. Angeles Carnero and Loriano Mancini are also gratefully acknowledged for their Matlab codes. The first two authors also acknowledge support from Laboratory EPIFISMA.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Carlos Trucíos  http://orcid.org/0000-0001-8746-8877

Luiz K. Hottta  http://orcid.org/0000-0002-1005-602X.

Esther Ruiz  http://orcid.org/0000-0002-5944-9449.

Additional information

Funding

The first two authors acknowledge financial support from the São Paulo Research Foundation (FAPESP) grants [2012/09596-0], [2013/00506-1] and [2013/23524-5]. The second author also acknowledges financial support from Coordination for the improvement of Higher Education Personnel (CAPES) grant [10600/13-2] while the third author is grateful for financial support from Project ECO2012-32401 and ECO2015-70331-C2-2-R (MINECO/FEDER) by the Spanish Government.