Parameter Estimation of Binned Hawkes Processes

A key difficulty that arises from real event data is imprecision in the recording of time-stamps. In many cases, retaining times with a high precision expensive due to sheer volume activity. Combined practical limits on accuracy measurements, binned common. order use point processes model such data, tools for handling parameter estimation are essential. Here we consider Hawkes process, type self-exciting process has found application modeling financial stock markets, earthquakes and social media cascades. We develop novel optimization approach using modified Expectation-Maximization algorithm, referred as Binned Expectation Maximization (BH-EM). Through detailed simulation study, demonstrate existing methods capable producing severely biased highly variable estimates our BH-EM method significantly outperforms them all studied circumstances. further illustrate performance network flow (NetFlow) between devices large-scale computer network, characterize triggering behavior. These results highlight importance correct data. Supplementary materials this article available online.