Abstract

Hawkes processes are a type of point processes which model self-exciting and mutually- exciting behaviour of events. They have a wide variety of applications in seismology, epidemiology, financial markets and even social media cascades. However, acquiring real- life data comes with a lot of inaccuracies since the event times might have been rounded. This leads to considering the data as binned event times instead. Modelling real-world scenarios using point processes increases the necessity for methods to estimate the true parameters of the model from the observed binned data. We present a novel application of the debiased Whittle estimation technique on univariate Hawkes processes, alongside an improvement of the standard Whittle through tapering and differencing. Using a thorough simulation study, we compare the performance of the methods developed in our work to the already existing ones which produce estimates with similar bias at the cost of longer computational time. We also investigate the possibility of extending the algorithms derived for the multivariate case, noticing promising results.

Andrew Connell

Graduate Mathematician & Statistician

My research interests include signal processing, time series analysis and point processes.