Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. GARCH modelling in continuous time for irregularly spaced time series data
 Bernoulli 14 (2008), Nr.2, S.519542 ISSN: 13507265 

 Englisch 
 Zeitschriftenaufsatz 
 Fraunhofer ITWM () 
Abstract
The discretetime GARCH methodology which hits had such a profound influence on the modelling of heteroscedasticity in time series is intuitively Well motivated in capturing many 'stylized facts' concerning financial series, and is now almost routinely used in a wide range of situations, often including some where the data are not observed at equally spaced intervals of time. However, such data is more appropriately analyzed with a continuoustime model which preserves the essential features of the successful GARCH paradigm. One possible such extension is the diffusion limit of Nelson, but this is problematic in that the discretetime GARCH model and its continuoustime diffusion limit tire not statistically equivalent. As till alternative, Kluppelberg et al. recently introduced a continuous.time version of the GARCH (the 'COGARCH' process) which is constructed directly from a background driving Levy process, The present paper how to fit this model to irregularly spaced time series data using discretetime GARCH methodology, by approximating the COGARCH with an embedded sequence of discretetime, GARCH series which converges to the continuoustime model in a strong sense (in probability, in the Skorokhod metric), as the discrete/approximating grid grows finer. This property is also especially useful in certain other applications, such as options pricing. The way is then open to using, for the COGARCH, similar statistical techniques to those already worked out for GARCH models and to illustrate this, an empirical investigation using stock index data is carried out.