Self-similarity in financial markets: A fractionally integrated approach

This study discussed the self-similar processes using the fractionally integrated methodology in three selected global financial equity markets. Under the heavy-tailed assumption, the symmetric and asymmetric fractionally integrated time varying volatility is developed by selecting the most appropriate power transformation of the volatility proxy. The empirical studies included the subprime mortgage crisis and its impact on the selected equity markets. The preliminary analysis indicated that the fractional differencing coefficients have a tendency to reduce the long memory for all the indices when the power of the absolute return increased from unity to two. Our empirical results evidenced that the power conditional standard deviation modeling outperformed the conditional variance specification across the indices. It is also found that the subprime mortgage crisis provided significant improvement in the volatility persistence and further leverage effect to all the indices.