Statistical inference for alpha-series process with truncated normal distribution

In this paper we consider an alpha-series process when the distribution of the first occurrence time of an event is assumed to be truncated normal distribution. Firstly, we study several nonparametric inferences including the Least-square estimate (LSE) and the Maximum-likelihood estimate (ML). Some estimators of the parameters in alpha-series process are derived by using the methods referred above. Furthermore, we consider the consistency and asymptotic normality properties of the estimators. Finally, we obtain the simulation results which are calculated over Monte Carlo replications to compare the performance of these variety estimators.