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We present the construction of a (semi-parametric) M-estimator for the period of a non-homogeneous Poisson process with a periodical intensity function. We address the issues of identifiably of this parameter, consistency of estimator, rate of convergence and discuss the severity of the conditions under which these results hold further making some connections with ergodic theory. Some simulations will be shown to exemplify the workings of the estimator. We also make a short comparison with estimators proposed in the past for the period. Further, we present a quick sight at ongoing work to develop an iterative procedure for improving the rate of convergence of the estimator based on estimating large multiples of the period; if successful, this procedure will allow us to obtain convergence rates arbitrarily close to the optimal rate which is known to be n{3/2}.
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