Bootstrap‎, ‎Modified Maximum Likelihood and Moment Estimators Comparison for Parameters of Autoregressive Model with Non-negative Residuals

Normal residual is one of the usual assumptions in autoregressive model but sometimes in practice we are faced with non-negative residuals. In this paper, we have considered the autoregressive time series model where the residuals follow exponential and Weibull family. The estimation of the parameters in autoregressive with non-negative residuals are studied based on the modified maximum likelihood, bootstrap and moments estimators. We examine by simulation, the performance of the proposed estimation methods and found that the bootstrap estimator is the better one for autoregressive model with non-negative residuals. As a real data analysis, we have considered the S&P500 data between 1987-2015 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.