Moment and memory properties of linear conditional heteroscedasticity models, and a new model
University of Exeter (Cardiff Business School at time of writing)
Journal of Business & Economic Statistics
American Statistical Association
This article analyses the statistical properties of that general class of conditional heteroscedasticity models in which the conditional variance is a linear function of squared lags of the process. GARCH, IGARCH, FIGARCH, and a newly proposed generalization, the HYGARCH model, belong to this class. Conditions are derived for the existence of second and fourth moments, and for the limited memory condition of near-epoch dependence. The HYGARCH model is applied to 10 daily dollar exchange rates, and also to data for Asian exchange rates over the 1997 crisis period. In the latter case, the model exhibits notable stability across the pre-crisis and post-crisis periods.
Research supported by ESRC grant L138251025
Pre-print dated April 2003
Journal of Business & Economic Statistics, Vol. 22 (1) 2004 , pp. 16-29