# MLE of Hawkes' self-exciting point processes

T.Ozaki’s paper titled, “Maximum likelihood estimation of Hawkes' self-exciting point processes”, deals with the univariate Hawkes’ process. The paper gives a detailed method to obtain the ML estimates of the process. In order to verify the ML estimates, the author simulates the process and compares the true vs. estimated parameters. I found a typo in one of the expressions for the gradient. In any case, R provides * nlm* function, that computes the gradient and hessian numerically. So, if one chooses to, one can slog out the expressions for gradient and hessian, and then feed in to

*, else, you can allow the function to do the job numerically.*

**nlm**The following document contains some ** R** code that I have written to estimate the parameters for Hawkes’ process. A good way to check whether the parameter estimation has gone right is by plotting a particular time changed process that should result in standard Poisson. It is easy to work out the compensator, given that the paper gives a clear explanation of all the necessary expressions.