This study proposes a new version of the Autoregressive Integrated Moving Average (ARIMA) model using Artificial Neural Networks (ANNs) denoted by ARIMA-NN. The new model incorporates a multi-layer perceptron with matrix multiplication within a feed-forward network. The logistic, hyperbolic tangent (tanh), and sigmoid activation functions are used for weight updates in ARIMA-NN. A new forecasting algorithm is proposed, and one-step and multiple-steps forecasting procedures are rigorously analyzed. The proposed model was evaluated against existing forecasting model using performance metrics such as the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to assess its effectiveness. The U.S. Census Bureau (www.census.gov) provides a data set of monthly drug sales spanning ten years (2014-2024), which is utilized in the study. The ARIMA-NN model is applied to generate forecasts for drug sales in the U.S. for the next four years to demonstrate the models' utility and efficacy. All the computations and visualizations are performed using various R packages in version 4.3.2.
