Separated hypotheses testing for autoregressive models with non-negative residuals

ABSTRACT

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 derived modified maximum likelihood estimators of parameters of the residuals and autoregressive coefficient. Also asymptotic distribution of modified maximum likelihood estimators in both stationary and non-stationary models are computed. So that, we can derive asymptotic distribution of unit root, Vuong's and Cox's tests statistics in stationary situation. Using simulation, it shows that Akaike information criterion and Vuong's test work to select the optimal autoregressive model with non-negative residuals. Sometimes Vuong's test select two competing models as equivalent models. These models may be suitable or unsuitable equivalent models. So we consider Cox's test to make inference after model selection. Kolmogorov–Smirnov test confirms our results. Also we have computed tracking interval for competing models to choosing between two close competing models when Vuong's test and Cox's test cannot detect the differences.

KEYWORDS:

• Akaike information criterion
• autoregressive model
• Cox's test
• model selection
• modified maximum likelihood
• tracking interval
• unit root test
• Vuong's test

Acknowledgments

We would like to thank the Editor and referees for their valuable comments and suggestions that have greatly improved the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

The authors advise no direct funding is associated with the research reported in this article.