Quasi maximum likelihood estimation and prediction in the compound Poisson ECOGARCH(1,1) model

Czado, Claudia and Haug, Stephan (2006): Quasi maximum likelihood estimation and prediction in the compound Poisson ECOGARCH(1,1) model. Collaborative Research Center 386, Discussion Paper 516

Abstract

This paper deals with the problem of estimation and prediction in a compound Poisson ECOGARCH(1,1) model. For this we construct a quasi maximum likelihood estimator under the assumption that all jumps of the log-price process are observable. Since these jumps occur at unequally spaced time points, it is clear that the estimator has to be computed for irregularly spaced data. Assuming normally distributed jumps and a recursion to estimate the volatility allows to define and compute a quasi-likelihood function, which is maximised numerically. The small sample behaviour of the estimator is analysed in a small simulation study. Based on the recursion for the volatility process a one-step ahead prediction of the volatility is defined as well as a prediction interval for the log-price process. Finally the model is fitted to tick-by-tick data of the New York Stock Exchange.

• Item Type: Paper
• Form of publication: Preprint
• Keywords: ECOGARCH; QMLE; L´evy process; leverage effect; prediction
• Faculties: Mathematics, Computer Science and Statistics > Statistics > Collaborative Research Center 386; Special Research Fields > Special Research Field 386
• Subjects: 500 Science > 510 Mathematics
• Language: English