B1313
Title: Mixture modelling for temporal point processes with memory
Authors: Xiaotian Zheng - University of Wollongong (Australia) [presenting]
Athanasios Kottas - University of California Santa Cruz (United States)
Bruno Sanso - University of California Santa Cruz (United States)
Abstract: A constructive approach is presented for building temporal point processes that incorporate dependence on their history. The dependence is modelled through the conditional density of the duration, i.e., the interval between successive event times, using a mixture of first-order conditional densities for each lagged duration. Such formulation for the conditional duration density accommodates high-order dynamics, and the implied conditional intensity function admits a representation as a local mixture of first-order hazard functions. By specifying the appropriate families of distributions for the first-order conditional densities with different shapes for the associated hazard functions, self-exciting or self-regulating point processes can be obtained. The method specifying a stationary marginal density is developed from the perspective of duration processes. The resulting model, interpreted as a dependent renewal process, introduces high-order Markov dependence among identically distributed durations, while extensions to cluster point processes are provided. These can describe duration clustering behaviors attributed to different factors, expanding the scope of the modelling framework to a wider range of applications. Regarding implementation, a Bayesian approach for inference and model checking is developed. The model properties are analytically investigated, and the methodology is illustrated with data examples from environmental science and finance.
