The paper, written by Yosihiko Ogata, titled, ``On Lewis Simulation Method for Point Process", gives a detailed procedure to simulate univariate and multivariate point processes. The following document contains the algo and necessary R code for simulating univariate Hawkes' self exciting process. The good thing about this algo is that is based on “thinning” and hence it is not a computationally expensive task. Simulation of univariate Hawkes via Thinning

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.

Today, I had a chance to see a play, “Kuchh Bhi Ho Sakta Hai”. It is a one person act and in this case, it is Anupam Kher, who narrates his own life story in a way that keeps the audience entertaining right through. There was not a single dull moment in the entire play. Thoroughly entertaining 2 hour act.

Homogeneous Poisson process (HPP) is easy to simulate in R as there are standard functions built in to the language. Simulating Non-Homogeneous Poisson process(NHPP) take a little bit of effort. There are many algorithms out there and I guess the best amongst them is based on “thinning”. The math behind thinning is explained in the paper,”Simulation of NonHomogeneous Poisson Process by Thinning”. The paper, while explaining the method, also gives a laundry list of methods that can be used to simulate NHPP.

Via Barrons The world has a way of making what was once controversial safe for consumption. For evidence, look no further than Lou Reed’s upcoming induction into the Rock and Roll Hall of Fame. The same holds true for Virtu Financial, which successfully completed its initial public offering last week. That Virtu (ticker: VIRT) is now a publicly traded company is a marvel, considering the failure of its first attempt about a year ago.