ASSESSING THE PERFORMANCE OF ARIMA AND ARFIMA MODELS IN FORECASTING INTERNALLY GENERATED REVENUE OF KADUNA STATE

  • Muhammad Idris Usman Aliko Dangote University of Science and Technology Wudil, Kano
  • Tasi’u Musa Ahmadu Bello University, Zaria
  • Auwalu Ibrahim Aliko Dangote University of Science and Technology, Wudil
Keywords: ARIMA Model, ARFIMA model, Forecasting, Internally generated revenue

Abstract

Internally generated revenue (IGR) is an important source of revenue that can be used to fund public services and infrastructure projects. Accurate forecasting of IGR is essential for effective budgeting and financial planning. This study assessed the performance of ARIMA and ARFIMA models in forecasting internally generated revenue of Kaduna State. The study uses monthly IGR data from January 2003 to December 2023. The stationarity of the data was assessed using Augmented Dickey Fuller (ADF) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests. The findings showed that both ARIMA and ARFIMA models perform well in forecasting IGR, but ARFIMA model outperforms ARIMA model in terms of mean squared error (MSE), root mean squared error (RMSE), and mean absolute error (MAE). The generated forecast values for 24 months using the model revealed that out-sample IGR forecasts fluctuated (decreasing and increasing). Thus, the study recommends the use of ARFIMA model for forecasting IGR in Kaduna State for better revenue planning and economic policy formulation.

References

Ajisola, A. S. (2023). An Efficient Time Series Model for Tax Revenue Forecasting: A Case of Nigeria (Doctoral dissertation, AUST).

Atoyebi, S. B., Olayiwola, M. F., Oladapo, J. O., & Oladapo, D. I. (2023). Forecasting Currency in Circulation in Nigeria Using Holt-Winters Exponential Smoothing Method. South Asian Journal of Social Studies and Economics, 20(1), 25-41.

Akaike, H. (1974). A New Look at the Statistical Model Identification. I.E.E.E. Transaction on Automatic Control, 19, 716-723.

Alireza, E. & Ahmad, Y.S. (2009). Long Memory Forecasting of Stock Prices Index using a Fractionally Differenced ARMA Model. Journal of Applied Sciences Research, 10, 1721-1731.

Azza, A. M. A., Auni, F. M. Z. & Wee, P. M. (2021). The Comparison between ARIMA and ARFIMA Model to Forecast Kijang Emas (Gold) Prices in Malaysia using MAE, RMSE and MAPE. Journal of Computing Research and Innovation, 6(3), 22-33.

Box, G. E. P. & Jenkins, G. M. (1976). Time Series Analysis: Forecasting and Control. San Franciso: Holden- Day.

David, A. K., Enobong, F. U., & Damian, O. (2024). Volatility Analysis of Crude Oil Prices in Nigeria. FUDMA Journal of Sciences (FJS), 8(1), 125 134. https://fjs.fudutsinma.edu.ng

Dickey, D. A. & Fuller, W. A. (1979). Distributions of the Estimators for Autoregressive Timse Series with a Unit Root. Journal of the American Statistical Association, 74: 427-431.

Elmezouar, C., Ibrahim. M. A., Ahmad, I. & Laksaci, A. (2021). Comparison of ARFIMA, ARIMA and Artificial Neural models to Forecasting the Total Fisheries Production in India. Journal of Animal & Plant Sciences, 31(5), 1477-1484.

Festus, A. (2019). Application of Time Series Analysis on Revenue Generation in Adamawa State, A Case Study of Adamawa State Board of Internal Revenue Yola, Nigeria. Adapoly Printing Venture, Yola.

Geweke, J. & Porter-Hudak, S. (1983). The Estimation and Application of Long Memory Time Series Models. Journal of Time Series Analysis. 4, 221-237.

Granger, C. W. J. & Joyeux, R. (1980). An Introduction to LongMemory Time Series Models and Fractional Differencing. Journal of Time Series Analysis, 1(1), 15-29.

Hannan, E. J. & Quinn, B. G. (1979).The Determination of the Order of an Autoregression. Journal of the Royal Statistical Society, 41, 190-195.

Harrison, E. E., Uchenna, I. A., Simon, I. A., Yellow, M. D. & Chinedu, R. I. (2014). Application of Seasonal Box-Jenkins Techniques for Modelling Monthly Internally Generated Revenue of Rivers State of Nigeria. International Journal of Innovative Science, Engineering & Technology (IJISET), 1(7), 122-126.

Hamzaoui, N. & Regaieg, B. (2017). The Long Memory Behaviour of the EUR/USD Forward Premium. International Journal of Economics and Financial Issues, 7(3), 437-443.

Hosking, J.R.M. (1981). Fractional Differencing. Biometrika, 68(1), 165-176.

Jibrin, S.A., Musa, Y., Samail, M. & Abdul, A. (2021). Comparing the performance of ARIMA and ARFURIMA Models in Forecasting Nigeria Stock Price Index. Sule Lamido University Journal of Science and Technology (SLUJST), 2(2), 1-15

Kelkar, M., Borsa, C., & Kim, L. (2021). Time-Series Statistical Model for Forecasting Revenue and Risk Management. Journal of Student Research, 10(3), 1-14.

Kwiatkowski, P .C. B. Phillips, P. Schmidt, & Yongoheol, S. (1992). Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root. Journal of Econometric, 54: 159-178.

Liu, K., Chen, Y. & Zhang, X. (2017). An Evaluation of ARFIMA (Autoregressive Fractional Integral Moving Average). Programs Axioms, 6(16), 1-16.

Monge, M., & Infante, J. (2023). A Fractional ARIMA (ARFIMA) Model in the Analysis of Historical Crude Oil Prices. Energy Research Letters, 4(1), 112-121.

Nwakuya, M. T. & Biu, E. O. (2022). ARFIMA Modelling and Long Memory: The Case of Covid-19 Daily Deaths in Nigeria. International Journal of Innovative Mathematics, Statistics & Energy Policies, 10(4), 47-59.

Schwarz, K. J. (1978).The Determination of the Order of an Autoregression. Journal of the Royal Statistical Society, 41, 190-195.

Shittu, O.I. & Yaya, O.S. (2009). Measuring Forecast Performance of ARMA and ARFIMA Models: An Application to US Dollar/UK Pound Foreign Exchange Rate. European Journal of Scientific Research, 32(2):167-176.

Suleiman, M., Muhammad, I., Zakar, A. A., Zakari, Y. Iliyasu, R., Muhammad, A., Adamu, I. & Abdu, M. (2023). Modelling Nigeria Crude Oil Prices using ARIMA Time Series Models. NIPES Journal of Science and Technology Research, 5(1), 230-241.

Tasiu, M., Abdulrazak, U. and Hussaini, G. D. (2024). Modelling and Forecasting Nigeria's Tax Revenue: A Comparative Analysis of SARIMA and Holt-Winters Models. UMYU Scientifica, 3(3), 118 129.

Okorie, C.E., Ossai, F.C. & Ben, J. (2018). Time Series Analysis of Monthly Generated Revenue in Gombe Local Government. International Journal of Scientific and Innovative Mathematical Research, 6(2), 17-24.

Omekara, C.O., Okereke, O.E. & Ukaegeu, L.U. (2016). Forecasting Liquidity Ratio of Commercial Banks in Nigeria. Scientific Series, 3, 144-159.

Patrick, U. U. and John, E. E. (2013). Modeling Internally Generated Revenue (IGR) of Local Governments in Nigeria. Mathematical Theory and Modeling, 3(14), 23-29.

Uduma, E. A., Iwueze, S. I., Arimie, O. C. & Biu, O. E. (2021). Modelling the Nigerian Ports Authority Revenue Generated Series with and without Outliers. Academic Journal of Statistics and Mathematics (AJSM), 7(7), 16-39.

Wiri, L. & Lebari, G. T. (2022). Modelling of Nigeria Exchange Rate using Autoregressive Fractional Integrated Moving Average. Asian Journal of Pure and Applied Mathematics 4(1), 28-35.

Zhang, G. P. (2003). Time Series Forecasting using a Hybrid ARIMA and Neural Network Model. Neurocomputing, 50, 159175.

Published
2025-06-30
How to Cite
Usman, M. I., Musa, T., & Ibrahim, A. (2025). ASSESSING THE PERFORMANCE OF ARIMA AND ARFIMA MODELS IN FORECASTING INTERNALLY GENERATED REVENUE OF KADUNA STATE. FUDMA JOURNAL OF SCIENCES, 9(6), 193 - 201. https://doi.org/10.33003/fjs-2025-0906-3666