The Poisson regression model (PRM) is usually applied when the dependent variable is in the form of count data. The purpose of this study is to compare methods of estimation for the Poisson Regression
Model's first-order autocorrelation (AR(1)). The Kibria and Lukman Estimator Method (KL), Generalized Least Square Estimator Method (GLS), the Liu Estimator Method (LE), and the Reduction Liu Estimator Method (RLE) were employed. Monte Carlo simulations are used to compare these methods. The data generated follows Poisson
Regression Model, however, because of sample size and autocorrelation levels among other things, to create a first-order
autocorrelation among random errors. The Mean square Error (MSE) criterion was used for comparison. The methods are also evaluated on actual data, moreover, the findings demonstrated that the KL approach is superior to the other estimation techniques in terms of its performance.