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Pruscha, H. (1998): Semiparametric Point Process and Time Series Models for Series of Events. Collaborative Research Center 386, Discussion Paper 114
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Abstract

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.