Procesy s dlouhou pamětí a jejich vývoj ve výnosech indexu PX v letech 1999 – 2009

Long-term memory processes have been extensively examined in recent literature as they provide simple way to test for predictability in the underlying process. However, most of the literature interprets the results of estimated Hurst exponent simply by its comparison to its asymptotic limit of 0.5. Therefore, we present results of Monte Carlo simulations for rescaled range, modified rescaled range and detrended fluctuation analysis based on chosen scales taken into consideration. The results of simulations show that even independent process can show Hurst exponent far from 0.5. In our analysis of evolution of Hurst exponent between 1999 and 2009, we show that Czech PX experienced persistent behavior which weakened in time. Nevertheless, the returns of PX remain close to confidence interval separating independent and persistent behavior.