Hi,assume I have a time-series which describes the frequency of an event in a given time interval.e.g. [$]\{Y_t\}_{t=1,2,\ldots}[$] says that in the year [$]t[$] the frequency of the event is [$]Y_t\in(0,1)[$].Now assume that I want to model event process in continuous by a Poisson process with time-varying intensity, where the intensity is namely a square root process.I would know what is the map between the instantaneous intensity and the frequency time-series and which is the correct wat to estimate the square root process parameters (average, reversion speed and volatility scale) from the frequency time-series. Since the time-series is yearly, I consider one year as the unit of time meausure in the continuous time dynamics (i.e. parameters are yearly parameters).I suppose I cannot simply match average, standard deviation and first order correlation but I should do something similar in the end.Can you help me please? thanks a lot!

The question sounds simple, but inference with latent variables can get quite involved. Googling something like "inference for cox processes" might turn up some clues.