Statistical Inference in Autoregressive Models with Non-negative Residuals

Normal residual is one of the usual assumptions of autoregressive models but in practice sometimes we are faced with non-negative residuals case.
In this paper we consider some autoregressive models with non-negative residuals as competing models and we have derived the maximum likelihood estimators of parameters based on the modified approach and EM algorithm for the competing models. Also, based on the simulation study, we have compared the ability of some model selection criteria to select the optimal autoregressive model. Then we consider a set of real data, level of lake Huron 1875-1930, as a data set generated from a first order autoregressive model with non-negative residuals and based on the model selection criteria we select the optimal model between the competing models.