Abstract This paper examines the long memory property in the conditional variance of the G7’s major stock market indices, using the FIGARCH model. The GARCH and IGARCH frameworks are also estimated for comparative purposes. To this end, a dataset encompassing the daily returns of the S&P/TSX 60, CAC 40, DAX 30, MIB 30, NIKKEI 225, FTSE 100 and S&P 500 indices from January 4th 1999 to January 21st 2009 is employed. Our results show evidence of long memory in the conditional variance, which is more pronounced for DAX 30, MIB 30 and CAC 40. However, NIKKEI 225 is found to be the less persistent. This may be explained by the fact that smaller markets, like DAX 30, are less liquid, less efficient, and more prone to experiencing correlated fluctuations and, therefore, more susceptible to being influenced by aggressive investors. On the other hand, bigger markets tend to exhibit lower correlations, thus favoring lower persistence levels. Finally, we use the log likelihood, Schwarz and Akaike Information Criteria to discriminate between models and found that FIGARCH is the most suitable model to capture the persistence.