Some Identification Methods of Mixed Model ARMA(1,1) and its Probabilistics Properties when Detetcting Random Error belong to Poisson Distribution

Most of the time series that appear in many economical geophysical and otherphenomenas are driven by non-Gaussian random error (at), so the aim of this paper is to investigate some of the probabilistic properties of Gaussian and non-Gaussian mixed model ARMA(1,1), and the identification methods of this model.The researchers have theoretically derived the characteristic function the first four moments and the skeweness and Kurtosis coeficients for (at) for Gaussian distribution and non-Gaussian distribution (poisson) and simulation experiment were used to confirm the accuracy of the theoretical results, We have also declared the identification sample autocorrelation function (ESACF) and (Kumar) method (c-table) depending upon the pade approximation and we have suggested a method depending upon the extended sample partial autocorrelation function (ESPACF) to ascertain the efficiency of suggested method.