ARIMA-NN Model for Drugs Sales Forecasting in the United States
Keywords:
ARMA , ARIMA , ANNs , Forecasting , Time Series , Multi-layer PerceptronAbstract
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 dataset 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.
References
[1] Alsheheri, G.; "Comparative Analysis of ARIMA and NNAR Models for Time Series Forecasting". J. Appl. Math. Phys., 13 (1): 267–280, 2025.
[2] Kaur, J.; Parmar, K. S.; Singh, S.; "Autoregressive models in environmental forecasting time series: a theoretical and application review". Environ. Sci. Pollut. Res., 30 (8): 19617–19641, 2023.
[3] Verma, P.; Reddy, S. V; Ragha, L.; Datta, D.; "Comparison of time-series forecasting models". in 2021 International Conference on Intelligent Technologies (CONIT) 1–7, IEEE:, 2021.
[4] Zhang, G. P.; "Time series forecasting using a hybrid ARIMA and neural network model". Neurocomputing, 50: 159–175, 2003.
[5] Dubey, A. K.; Kumar, A.; García-Díaz, V.; Sharma, A. K.; Kanhaiya, K.; "Study and analysis of SARIMA and LSTM in forecasting time series data". Sustain. Energy Technol. Assessments, 47: 101474, 2021.
[6] Shmueli, G.; Polak, J.; ‘Practical Time Series Forecasting with r: A Hands-on Guide’. 2nd ed Axelrod schnall publishers:, Rockville, MD, USA, 2024.
[7] Diggle, P.; Giorgi, E.; Time Series: A Biostatistical Introduction. 1st ed, Oxford University Press:, Oxford, UK, 2025.
[8] Asparouhov, T.; Muthén, B.; "Comparison of models for the analysis of intensive longitudinal data". Struct. Equ. Model. A Multidiscip. J., 27 (2): 275–297, 2020.
[9] Singh, V. P.; Singh, R.; Paul, P. K.; Bisht, D. S.; Gaur, S.; "‘Hydrological Processes Modelling and Data Analysis’". Water Sci. Technol. Libr., 127: 105–120, 2024.
[10] Brockwell, P. J.; Davis, R. A.; ‘Time Series: Theory and Methods’. Springer science & business media:, New York, USA, 1991.
[11] Alsuwaylimi, A. A.; "Comparison of ARIMA, ANN and Hybrid ARIMA-ANN models for time series forecasting". Inf. Sci. Lett., 12 (2): 1003–1016, 2023.
[12] Wagner, B.; Cleland, K.; "Using autoregressive integrated moving average models for time series analysis of observational data". bmj, 383: 2023.
[13] Satrio, C. B. A.; Darmawan, W.; Nadia, B. U.; Hanafiah, N.; "Time series analysis and forecasting of coronavirus disease inp Indonesia using ARIMA model and PROPHET". Procedia Comput. Sci., 179: 524–532, 2021.
[14] Beeram, S.R.; Kuchibhotla, S.; "Time Series Analysis on Univariate and Multivariate Variables: A Comprehensive Survey". In: Proceedings of the 11th International Conference on Communication Systems and Networks (COMSNETS INDIA 2019), Bengaluru, India, 7–11 January 2019; IEEE, Eds.; IEEE: New York, NY, USA, 2020.
[15] Tsay, R. S.; “Multivariate Time Series Analysis: With R and Financial Applications”. John Wiley & Sons:, 2013.
[16] Hajirahimi, Z.; Khashei, M.; "A novel parallel hybrid model based on series hybrid models of ARIMA and ANN models". Neural Process. Lett., 54 (3): 2319–2337, 2022.
[17] Jafarian-Namin, S.; Shishebori, D.; Goli, A.; "Analyzing and predicting the monthly temperature of tehran using ARIMA model, artificial neural network, and its improved variant". J. Appl. Res. Ind. Eng., 11 (1): 76–92, 2024.
[18] Elsaraiti, M.; Merabet, A.; "A comparative analysis of the arima and lstm predictive models and their effectiveness for predicting wind speed". Energies, 14 (20): 6782, 2021.
[19] He, R.; Zhang, L.; Chew, A. W. Z.; "Modeling and predicting rainfall time series using seasonal-trend decomposition and machine learning". Knowledge-Based Syst., 251: 109125, 2022.
[20] Cheng, C.; Sa-Ngasoongsong, A.; Beyca, O.; Le, T.; Yang, H.; Kong, Z.; Bukkapatnam, S. T. S.; "Time series forecasting for nonlinear and non-stationary processes: a review and comparative study". Iie Trans., 47 (10): 1053–1071, 2015.
[21] Ahmed, S.; Nielsen, I. E.; Tripathi, A.; Siddiqui, S.; Ramachandran, R. P.; Rasool, G.; "Transformers in time-series analysis: A tutorial". Circuits, Syst. Signal Process., 42 (12): 7433–7466, 2023.
[22] Sun, F.; Meng, X.; Zhang, Y.; Wang, Y.; Jiang, H.; Liu, P.; "Agricultural product price forecasting methods: A review". Agriculture, 13 (9): 1671, 2023.
[23] Abbas, M.K.; Mahdi, G.J.; Mseer, H.A.H.; "A Multivariate Bayesian Model Using Gibbs Sampler with Real Data Application". In: Proceedings of the AIP Conference, Baghdad, Iraq, 2024; AIP Publishing: Melville, NY, USA, 2024.
[24] Abbas, I. T.; Ghayyib, M. N.; "Using Sensitivity Analysis in Linear Programming with Practical Physical Applications". Iraqi J. Sci., 907–922, 2024.
[25] Mseer, H.A.H.; Mahdi, G.J.M.; "Comparison Among Variable Selection Models and Its Application to Health Dataset". In: Proceedings of the AIP Conference, Baghdad, Iraq, 2023; AIP Publishing: Melville, NY, USA, 2023.
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