  We introduce a new model which can be considered as a extended version of the
Hawkes process in a discrete sense. This model enables the integration of
various residual distributions while preserving the fundamental properties of
the original Hawkes process. The rich nature of this model enables a filtered
historical simulation which incorporate the properties of original time series
more accurately. The process naturally extends to multi-variate models with
easy implementations of estimation and simulation. We investigate the effect of
flexible residual distribution on estimation of high frequency financial data
compared with the Hawkes process.
