This article examines the power of two well-known procedures of fractional integration in the context of conditional heteroskedasticity in the variance. One of the methods is parametric while the other is semiparametric. Several Monte Carlo experiments conducted in this article show that both methods perform well to detect the order of integration of the series under the assumption that the underlying disturbances follow Generalized Autoregressive Conditional Heteroscedasticity (GARCH)-type errors. The methods are applied to 10 European stock market indices. The results indicate that the orders of integration of the series are close to 1 in all cases, being strictly higher than 1 in four countries. Moreover, taking the d-differenced processes, and estimating Fractionally Integrated GARCH (FI-GARCH) models on the squared residuals, fractional degrees of integration are obtained in the majority of the series.