This study aims to investigate the features of the container freight indices when there is a long memory effect. We employed GPH test, GSP test, the Rescaled Range Tests of Mandelbrot (1972) and Lo (1991), FIGARCH, HYGARCH and FIAPARCH models for the long memory test and estimation. Our results suggest that precise estimates of container freight indices may be acquired from a long memory in volatility models with Student-t and skewed Student-t distribution. Such models might improve the longterm volatility forecast and more precise pricing of container freight contracts. We could extend these findings to the risk management in the container freight markets. Moreover, for appropriate risk evaluation of container freight indices, the degree of persistence should be examined and appropriate modelling that includes volatility clustering, asymmetry, leptokurtosis and long range dependence should be take into consideration. We could extend this implication to the connection of the container freight market management.