Inference for Nonstationary Self-Exciting Point Processes

• Activity Number: 644
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Feng Chen*+ and Peter Gavin Hall
• Companies: The University of New South Wales and University of Melbourne
• Keywords: Hawkes process ; point process ; self-exciting ; asymptotics

Abstract

The classical self-exciting process of Hawkes is a stationary point process in which the intensity process is expressed as constant background event intensity plus the contributions of past events of the process. In some applications, especially where the amount of data to model is large, the constant background event intensity assumption seems rather restrictive, and the resulting model fit unacceptable. The extended self-exciting process where the background event intensity is allowed to vary over time seems a natural alternative model in such situations. In this talk we consider inference procedures for a nonstationary self-exciting process where the background intensity is time-varying. Two cases are treated -- the first with a parametric background intensity, and the second with a background intensity only assumed to be a positive smooth function of time. In both cases, the parametric form of the excitation function is assumed known. We consider the maximum likelihood and least square estimators in the first case and a local linear profiling likelihood estimator in the second case. Application is illustrated with ultra-high frequency stock trading data.