Rampant terrorism poses a serious threat to the national security of many countries worldwide, particularly due to separatism and extreme nationalism. This paper focuses on the development and application of a temporal self-exciting point process model to the terror data of three countries: the US, Turkey, and the Philippines. To account for occurrences with the same time-stamp, this paper introduces the order mark and reward term in parameter selection. The reward term considers the triggering effect between events in the same time-stamp but different order. Additionally, this paper provides comparisons between the self-exciting models generated by day-based and month-based arrival times. Another highlight of this paper is the development of a model to predict the number of terror events using a combination of simulation and machine learning, specifically the random forest method, to achieve better predictions. This research offers an insightful approach to discover terror event patterns and forecast future occurrences of terror events, which may have practical application towards national security strategies.