GARCH modelling in continuous time for irregularly spaced time series data

Economy – Quantitative Finance – Statistical Finance

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Published in at http://dx.doi.org/10.3150/07-BEJ6189 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

10.3150/07-BEJ6189

The discrete-time GARCH methodology which has 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 continuous-time 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 discrete-time GARCH model and its continuous-time diffusion limit are not statistically equivalent. As an alternative, Kl\"{u}ppelberg et al. recently introduced a continuous-time version of the GARCH (the `COGARCH' process) which is constructed directly from a background driving L\'{e}vy process. The present paper shows how to fit this model to irregularly spaced time series data using discrete-time GARCH methodology, by approximating the COGARCH with an embedded sequence of discrete-time GARCH series which converges to the continuous-time 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.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

GARCH modelling in continuous time for irregularly spaced time series data does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with GARCH modelling in continuous time for irregularly spaced time series data, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and GARCH modelling in continuous time for irregularly spaced time series data will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-56094

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.