Non-Nested Model Selection in Regression Models with Non-Negative Time Series Residual

Normality hypothesis and independence of residuals are the usual assumptions for re- gression models. But in practice, sometimes we are faced with non- negative autocorrelated residuals case.
This paper discuss the problem of model selection for regression model with non-negative autoregressive residuals, Among the non-negative distributions, we consider, Gamma,Weibull, Log-normal distributions as rival models.We have derived the modified maximum likelihood estimators as efficient alternative for estimating model parameters. Finallyý, ýusing simulation,we try to choose the optimal regression model with non-negative autoregressive residuals by comparing the ability of some model selection criteriaý.