MODELING COVID-19 AND PARAMETERS ESTIMATION OF HAWKES PROCESS

This paper deals with the study of stochastic self-exciting processes called Hawkes processes, where many accidents during their occurrence usually form data over time represented by the so-called cluster events, meaning that the occurrence of the event is represented by cluster samples in which the occurrence of each event stimulates the occurrence of another event at an accelerated rate is similar to a cluster. Hawkes processes are a type of stochastic processes that can be classified in many types of data that are characterized by their occurrence followed by the occurrence of accidents in an accelerated manner, such as the occurrence of aftershocks after certain earthquake or the occurrence of trading operations in a stock market or stock market after a certain jump in trading as a result of a certain circumstance, which drives market traders to tend towards speculations, whether by buying or selling. That is, Hawkes processes are stochastic processes that depend in their analysis of accidents on the effects resulting from the occurrence of previous accidents, and this is what is called the effect of the self-exciting of the event. Real data analysis was conducted to study the behavior of the behavior of the data of incidents of the number of people infected with the COVID-19 virus via Hawkes process. The estimation methods, DNMLL and AEMA, have used to estimate the Hawkes process parameters. The bias criterion and standard deviation have used to assess the performance of the estimation methods in terms of the quality of the estimators. The result shows the performance of the DNMLL method in estimation. In addition the Kolmogorov-Smirnov test have used ensure that the data follows the standard exponential distribution (Hawkes process), as well as testing the stationary of the Hawkes process b using the branching ration test.