We study in this paper the presence of long memory of four Mediterranean stock markets namely Morocco, Turkey, Spain, and France, over the period 2000-2020. The presence of long memory propriety has tested by using the R/S analysis approach. Results show that the four processes have a long memory. furthermore, ARFIMA-FIGARCH, under different distribution assumptions as Normal, Student-t, and Skewed Student- t, was estimated in order to test the feature of long memory in the return and volatility of the stock markets simultaneously. Results show strong evidence of long memory in both returns and volatility for the Moroccan and French stock markets and only in volatility for The Spanish and Turkish ones. The long memory in returns indicates that their behavior is predictable implying the rejection of the efficient market hypothesis. The long memory in volatility shows that risk is an important parameter of the behavior of the future returns in the four stock markets.

In our study we use the univariate and multivariate GARCH models to analyze the volatility behavior of the daily data of four Mediterranean stock markets (Morocco, Turkey, Spain, and France) spanning the period 2000-2020. We find a strong evidence of persisting of volatility in each of these markets. Results also indicate that both the univariate and the multivariate approaches capture well the ARCH and GARCH effects. We analyze the conditional covariances, and co-volatility spillovers between the Moroccan stock market and the three other Mediterranean stock markets. In order to study co-volatility spillovers, our work is built on the diagonal BEKK model especially the conditional covariances.