We are dealing with regression models for point processes having a multiplicative intensity process of the form alpha(t) * b_t . The deterministic function alpha describes the long-term trend of the process. The stochastic process b accounts for the short-term random variations and depends on a finite-dimensional parameter. The semiparametric estimation procedure is based on one single observation over a long time interval. We will use penalized estimation functions to estimate the trend alpha,

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... while the likelihood approach to point processes is employed for the parametric part of the problem. Our methods are applied to earthquake data as well as to records on 24-hours ECG.