When there is a high correlation between observations of the past and far future and their relationship is not negligible, the time series under study is characterized by long memory. The presence of long memory in a time series has many potential applications in various fields of finance. In this study, the presence of long memory in return series of the insurance, banking, petroleum products, textiles, chemicals and agriculture is evaluated in Tehran Stock Exchange (the data for the period from 21/3/2009 to 21/3/2014) using the BDS test. Then the above test was confirmed by means of ARFIMA test. The results indicate that all studied parameters have a long memory. Finally, to confirm the presence of long memory in indexes, since the long-term memory makes its previous output dependent, a predictable parameter can be found in dynamic time series. This characterization is a reason for rejecting the weak form of efficient market hypothesis