This study outlines distributional properties and tests the applicability o
f different models for the ISEQ index and its major constituents. A Stabili
ty under Additions procedure is applied to raw, filtered and rescaled retur
ns. The filtering process uses GARCH(1, 1) and GARCH-M(1, I) specifications
, removing the influence of temporal anomalies and non-synchronous trading
effects. Rescaling involves the standardising of returns using the time var
ying models estimates of conditional variance. Results support the ordinary
stable and mixtures of stables distributions. The lack of normality is aff
ected by first and second moment dependence.