I have stumbled on to a few mini-projects that revolve around fitting univariate and bivariate Hawkes processes. In this post, I will briefly summarize the write ups : High Frequency Trade Prediction with Bivariate Hawkes Process The authors starts with a SDE for intensity process and formulate its solution as a univariate Hawkes process. A visual depiction of self-excited intensity process is obtained via simulation. The time change theorem is stated and a QQ plot of the compensator is shown to follow an exponential inter-arrival distribution.

The paper titled, “Self-Exciting Point Process Models of Civilian Deaths in Iraq”, deals with fitting point processes to civilian deaths from March 2003 to December 2007. In this post, I will summarize main points from the paper Firstly, What is “Operation Iraqi Freedom” ? Here’s a wiki blurb The 2003 invasion of Iraq lasted from 19 March to 1 May 2003 and signaled the start of the conflict that later came to be known as the Iraq War, which was dubbed Operation Iraqi Freedom by the United States.

The paper, written by Ioane Muni Toke and Fabrizio Pomponio, titled, Modeling Trades-Through in a Limit Order Book Using Hawkes Processes, uses Hawkes process to examine microstructure behavior. This paper uses Multivariate Hawkes process to model trades-through. The best thing about this paper is that the authors have made the dataset available for the readers so that they can work through the numbers and get a feel of model inference. The dataset is available at dataverse.

Via TP (Techcrunch) : Today, Silicon Valley is the hottest place for quants to be – though people with this skill set are often referred to now as data scientists. A similar confluence of factors — data, technology and algorithms — has combined to enable a new class of transformational opportunities. These opportunities are not limited to just financial services; they are showing up in every sector of the economy.

The following document contains a brief summary of the paper titled, “Autoregressive Conditional Duration - A New Model for Irregularly Spaced Transaction Data” by Engle and Russell. ACD-Summary Takeaway : The paper models the duration between transactions.With the ease of availability of HF data, there needs to be a model that captures irregularly spaced timestamps. It is obvious that neither a standard Poisson process nor a non-homogeneous Poisson process is going to be a good fit.