Methods for Estimating the AR (1) Autoregressive Model Parameter for Data Following an Exponential Distribution

Section: Research Article
Issue
Vol. 35 No. 4 (2026): Volume 35, Issue 4
Pages
105-115

Abstract

This study aims to compare the performance of different estimation methods for a first-order autoregressive model (AR(1)) under the assumption that random errors do not follow a normal distribution but rather an exponential one. Four estimation methods were used: Bayesian, Jeffrey, Maximum Likelihood (MLE), and Least Squares (OLS), to evaluate their efficiency in estimating the model parameters.


The study was applied to real temperature data for Mosul, in addition to simulated data generated to verify the reliability of the results. The comparison between the methods was based on Mean Squared Error (MSE) and Akaiki Information Criterion (AIC).


The results showed that the best model performance was achieved at a value of ϕ=0, where the lowest values ​​for both AIC and MSE were obtained in both the real and simulated data, indicating no significant time dependence in the studied series. The results also showed that Bayesian methods have higher flexibility and stability compared to traditional methods, especially under the assumption of an exponential distribution of errors.

Keywords:

autoregressive, Bayes, exponential distribution, Fisher Information

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Authors

Elham Abdulkreem Hussain

Northern Technical University, Administrative Technical College, Mosul, Iraq

Ahmad.N.S. Al-Shallawi

Northern Technical University, Administrative Technical College, Mosul, Iraq

Ammar Hazim Taha

Northern Technical University, Technical Management Institute, Mosul, Iraq

Identifiers

DOI: 10.33899/8wv0k731

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[1]
“Methods for Estimating the AR (1) Autoregressive Model Parameter for Data Following an Exponential Distribution”, JES, vol. 35, no. 4, pp. 105–115, Oct. 2026, doi: 10.33899/8wv0k731.
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How to Cite

[1]
“Methods for Estimating the AR (1) Autoregressive Model Parameter for Data Following an Exponential Distribution”, JES, vol. 35, no. 4, pp. 105–115, Oct. 2026, doi: 10.33899/8wv0k731.