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