Analysis of ‎Autoregressive ‎Models with ‎Dependent and non-Gaussian ‎Innovations

Zamani Mehreyan, Sedigheh; Hajrajabi, Arezo

doi:10.22034/aa.2026.2079612.1021

Analysis of ‎Autoregressive ‎Models with ‎Dependent and non-Gaussian ‎Innovations

Articles in Press

Document Type : Original Article

Authors

Sedigheh Zamani Mehreyan ¹

Arezo Hajrajabi ²

¹ Ghazvin

² Department of Statistics‎, ‎Imam Khomeini International University‎, ‎Qazvin‎, ‎Iran

10.22034/aa.2026.2079612.1021

Abstract

‎The assumption of independence and normality of ‎innovations‎ are usual assumptions in the study of time series models. But in some researches and studies, these assumptions cause limitations, in other words, we encounter cases where ‎the innovations‎ are not independent or do not follow the ‎Gaussian‎ distribution. In this Paper, we consider ‎autoregressive‎ model with dependent and non-‎Gaussian ‎innovations‎. It also is assumed that the true model is unknown, so we propose some competing models. The unknown parameters of competing models are estimated using the modified maximum likelihood method. Finally, by using information criteria, such as Akaike's information criteria and model selection tests such as Vuong's test, the optimal model has been selected. Using simulation, the performance of the modified maximum likelihood method has been studied and it has also been shown that the model selection criteria and tests select the closest model to the true model as the optimal model.

Keywords

Autoregressive model

Dependent innovations

Exponential family

Modified maximum likelihood estimation

Weibull family

Subjects