Marked point processes refer to time series of discrete events with additional information about the events. Seismic activities, neural activities, and price movements in financial markets are typical examples of marked point process data. In this paper, we propose a method for investigating the prediction limits of marked point process data, where random shuffle surrogate data with time window constraints are proposed and utilized to estimate the prediction limits. We applied the proposed method to the marked point process data obtained from several dynamical systems and investigated the relationship between the largest Lyapunov exponent and the prediction limit estimated by the proposed method. The results revealed a positive correlation between the reciprocal of the estimated prediction limit and the largest Lyapunov exponent of the underlying dynamical systems in marked point processes.