Semiparametric Point Process and Time Series Models for Series of Events

We are dealing with series of events occurring at random times
tau_n and carrying further quantitive information xi_n . Examples
are sequences of extrasystoles in ECG­records. We will present two
approaches for analyzing such (typically long) sequences (tau_n,
xi_n ), n = 1, 2, ... . (i) A point process model is based on an
intensity of the form alpha(t) * b_t(theta), t >= 0, with b_t a
stochastic intensity of the self­exciting type. (ii) A time series
approach is based on a transitional GLM. The conditional
expectation of the waiting time sigma_{n+1} = tau_{n+1} - tau_n is
set to be v(tau_n) * h(eta_n(theta)), with h a response function
and eta_n a regression term. The deterministic functions alpha and
v, respectively, describe the long-term trend of the process.