Self-weighted recursive estimation of GARCH models

ABSTRACT

The generalized autoregressive conditional heteroscedasticity (GARCH) processes are frequently used to investigate and model financial returns. They are routinely estimated by computationally complex off-line estimation methods, for example, by the conditional maximum likelihood procedure. However, in many empirical applications (especially in the context of high-frequency financial data), it seems necessary to apply numerically more effective techniques to calibrate and monitor such models. The aims of this contribution are: (i) to review the previously introduced recursive estimation algorithms and to derive self-weighted alternatives applying general recursive identification instruments, and (ii) to examine these methods by means of simulations and an empirical application.

KEYWORDS:

• GARCH
• High-frequency time series
• On-line estimation
• Recursive estimation
• Volatility.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F35
• 91G70

Acknowledgments

Authors would like to express special thanks to both anonymous referees for their helpful comments and suggestions.

Additional information

Funding

This research was supported by the grant GA P402/12/G097.