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Title: Time-varying graphs by locally stationary Hawkes processes Authors:  Hiroshi Shiraishi - Keio University (Japan) [presenting]
Taiga Uno - Keio University (Japan)
Yu Izumisawa - Keio University (Japan)
Junichi Hirukawa - Niigata University (Japan)
Abstract: Hawkes Graphs have been recently introduced to grasp the branching structure of multivariate stationary Hawkes processes. However, the existing procedure cannot describe the time structural changes, since stationary Hawkes processes are a class of stationary processes. We introduce a multivariate locally stationary Hawkes (lsHawkes) process, which is a natural extension of the univariate lsHawkes process. We first consider an approximation of the lsHawkes process by a time-varying integer-valued autoregressive (tvINAR) process. Then, we propose an estimation procedure for the time varying parameters based on the local least-squares method. Finally, we propose time-varying Hawkes graphs (tvHawkes graphs) by using the estimated parameters.