Hawkes süreçlerinin verimli simülasyonu

The aim of this study is to implement a fast and efficient algorithm to simulate Hawkes process whose intensity function depends on the events in its process history. In real life cases like seismology, disease spread, stock markets and social media, history (past events) affects future (next events). Hawkes process is suitable to model these cases with its history dependent conditional intensity function. Ogata's modified thinning algorithm is frequently used to simulate Hawkes processes. It is an inefficient algorithm especially for generating huge number of events for different purposes like statistical studies. A cluster-based (composition) algorithm simulating its sub-processes with inversion method using order statistic and time re-scaling theorem is proposed to the alternative of Ogata's modified thinning algorithm. Theoretical and empirical performance assessments are executed to compare the proposed cluster-based (composition) algorithm with the other algorithms and software in the literature. In the theoretical studies the number of operations which are required to generate Hawkes process events are identified and counted for different simulation algorithms to compare their performances. These operations are random variates, intensity function evaluations, inverse cumulative intensity function evaluations, comparison operations and sorting operations. For the empirical studies, a software of the proposed algorithm is implemented in R. This software is used to count the number of operations in the experiments. The results of the empirical studies justify theoretical studies. Furthermore, the time performance of the implemented software is compared with the software about Hawkes process simulation in the literature. The results of the theoretical and empirical studies show that the proposed algorithm is faster and more efficient compared to the other algorithms in the literature.