Data cloning estimation of GARCH and COGARCH models

Abstract

GARCH models include most of the stylized facts of financial time series and they have been largely used to analyse discrete financial time series. In the last years, continuous-time models based on discrete GARCH models have been also proposed to deal with non-equally spaced observations, as COGARCH model based on Lévy processes. In this paper, we propose to use the data cloning methodology in order to obtain estimators of GARCH and COGARCH model parameters. Data cloning methodology uses a Bayesian approach to obtain approximate maximum likelihood estimators avoiding numerically maximization of the pseudo-likelihood function. After a simulation study for both GARCH and COGARCH models using data cloning, we apply this technique to model the behaviour of some NASDAQ time series.

Keywords:

• GARCH model
• continuous-time GARCH process
• Lévy process
• COGARCH model
• data cloning
• Bayesian inference
• MCMC algorithm

AMS Subject Classification:

• C11
• C15
• C22

Acknowledgements

We thank the referees for their useful suggestions and valuable comments.

Funding

This research has been partially supported by grant [MTM2010-17323] (first author).