ESTIMATION OF THE DENSITY OF THE FILTERED POISSON IMPULSE PROCESS - APARAMETRIC APPROACH

We consider the Poisson driven pth order autoregressive (PDAR(p)) proc ess to be defined as the output of a continuous-time autoregressive sy stem, driven by a stationary Poisson impulse process. An explicit form ula for estimating the density of the Poisson impulse process is deriv ed by combining the second- and third-order cumulants of the discretiz ed PDAR (p) process. The validity of the proposed method is accessed t hrough Monte Carlo simulations in some specific examples.