Long-term memories in online users' selecting activities

• We find for the first time long-term correlations in online rating series.
• The long-term correlations are positively correlated with activity levels.
• The difference between subjective and objective behaviors distributes normally.
• We provide a new criterion to construct theoretical models.

In this paper, we investigate the long-term memory effect in the behavior of online users. Two user-oriented online movie systems are used in this study. Due to the short length of the series, the balanced estimation of diffusion entropy approach is used to evaluate scaling-invariance in selecting activities of users in the two online movie systems. Our results indicate that persistence (long-term memory) exists widely in the movie selecting series. However, there is generally significant difference between a user's objective and subjective behaviors. Additionally, statistically, the long-term memory depends on activity levels, as results show that the much more active a users' group, the stronger the long-term memory will be. These findings provide a new criterion for constructing reasonable models, and can help understand how individuals' behaviors form a collective behavior of an online society.