Modeling Inflation Dynamics with Atangana-Baleanu Fractional Derivatives: A Memory-Driven Approach to Consumer Price Index Forecasting

References

[1] Stock, J.H. & Watson, M.W. (2007). Why Has U.S. Inflation Become Harder to Forecast? Journal of Money, Credit and Banking, 39, 3–33. https://doi.org/10.1111/j.1538-4616.2007.00014.x

[2] Faust, J. & Wright J.H. (2013). Forecasting Inflation. Handbook of Economic Forecasting, 2(A), 2–56.

[3] Agina, P.C. & Echezona, G.N. (2022). Comparative analysis of the Gauss-Seidel and Jacobi methods for solving linear systems. COOU Journal of Physical Sciences, 5(1), 60–79.

[4] Diebold, F.X., & Rudebusch, G.D. (1989). Long memory and persistence in aggregate output. Journal of Monetary Economics, 24(2), 189–209. https://doi.org/10.1016/0304-932(89)90006-2

[5] Baillie, R. T. (1996). Long memory processes and fractional integration in econometrics. Journal of Econometrics, 73(1), 5–59. https://doi.org/10.1016/0304-4076(95)01732-1

[6] Granger, C.W.J., & Joyeux, R. (1980). An introduction to long-memory time series models and fractional differencing. Journal of Time Series Analysis, 1(1), 15–29. https://doi.org/10.1111/j.1467-9892.1980.tb00297.x

[7] Hosking, J.R.M. (1981). Fractional differencing. Biometrika, 68(1), 165–176. https://doi.org/10.1093/biomet/68.1.165

[8] Baillie, R.T., Chung, C.F., & Tieslau, M.A. (1996). Analysing inflation by the fractionally integrated Arfima-Garch model. Journal of Applied Econometrics, 11(1), 23–40. https://www.jstor.org/stable/2284951

[9] Gil-Alana, L.A. (2004). Long memory in the U.S. interest rate. International Review of Economics & Finance, 13(3), 265–276. https://doi.org/10.1016/j.iref.2003.05.002

[10] Pivetta, F. & Reis, R. (2007). The persistence of inflation in the United States. Journal of Economic Dynamics and Control, 31(4), 1326–1358. https://doi.org/10.1016/j.jedc.2006.05.001

[11] Kumar, V., Pansari, A. (2015). Measuring the Benefits of Employee Engagement. MIT Sloan Management Review, 56(4), 67–72.

[12] Podlubny, I. (1999). Fractional differential equations. California, CA: Academic Press.

[13] Atangana, A., & Baleanu, D. (2016). New fractional derivatives with non-local and non-singular kernel: Theory and application to heat transfer model. Thermal Science, 20(2), 763–769. https://doi.org/10.2298/TSCI160111018A

[14] Agina, P.C., Chukwuma, E.I., Chuka-Obidiegwu, B.E., Otugene, V.B., Ibeh, K.K., & Mbah, G.C.E. (2026). Local and Global Stability Analysis of the Disease-Free Equilibrium in a Fractional-Order Ebola Virus Transmission Model. International Journal of Applied Science and Mathematical Theory, 12(3), 30 – 48.

[15] Kilbas, A.A., Srivastava, H.M., & Trujillo, J.J. (2006). Theory and applications of fractional differential equations. Amsterdam, Netherlands: Elsevier.

[16] Scalas, E. (2006). The application of continuous-time random walks in finance and economics. Physica A: Statistical Mechanics and Its Applications, 362(2), 225–239. https://doi.org/10.1016/j.physa.2005.08.021

[17] Tarasov, V.E. (2011). Fractional dynamics: Applications of fractional calculus to dynamics of particles, fields and media. Springer. https://doi.org/10.1007/978-3-642-14003-7

[18] Agina, P.C., Chuka-Obidiegwu, B.E., Chukwuma, E.I., Ibeh, K.K., Otugene, V.B., Mbah, G.C.E. (2026). An Approximate Solution of a Fractional-order Epidemic Model using the Homotopy Perturbation Method. International Journal of Applied Science and Mathematical Theory, 12(3).

[19] Atangana, A., & Koca, I. (2016). Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order. Chaos, Solitons & Fractals, 89, 447–454. https://doi.org/10.1016/j.chaos.2016.02.012

[20] Otugene, V. B., Agina, P. C., Edogbanya, H., & Digwo, D. C. (2022). Existence and uniqueness analysis of Atangana-Baleanu fractional order network model of Noro virus. International Journal of Mathematical Analysis and Modelling, 5(2), 63–75.

[21] Otugene, V.B., Mbah, G.C.E, Owhenagbo, P., Idoko, P.I., Adedoyin, J.D., Enyejo, L.A., & Agina, P.C. (2024). Mathematical Analysis of Hepatitis B Virus Transmission Dynamics in the Absence of Therapy with Atangana-Baleanu Fractional-order SPQWXY Model. Journal of Advances in Mathematics and Computer Science, 39(11), 1–28.

[22] Gorenflo, R., Kilbas, A. A., Mainardi, F., & Rogosin, S. V. (2014). Mittag-Leffler func-tions, related topics and applications. Springer.

[23] Mainardi, F. (2010). Fractional calculus and waves in linear viscoelasticity. Imperial College Press.

[24] Caputo, M., & Fabrizio, M. (2015). A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications, 1(2), 73– 85.

[25] Losada, J., & Nieto, J.J. (2015). Properties of a new fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications, 1(2), 87–92.

[26] Box, G.E.P., Jenkins, G.M., Reinsel, G.C., & Ljung, G.M. (2015). Time series analysis: Forecasting and control. (5th ed.). Wiley.

[27] Harvey, A.C. (1990). Forecasting, structural time series models and the Kalman filter. Cambridge University Press.

[28] Tarasov, V.E. (2013). Review of some promising fractional physical models. International Journal of Modern Physics B, 27(9), 1330005. https://doi.org/10.1142/S0217979213300053

[29] Lina Song (2024). Dynamic Modeling and Simulation of Option Pricing Based on Fractional Diffusion Equations with Double Derivatives. Computational Economics, 65, 2205–2225.

[30] Monteiro, N.Z., dos Santos, R.W. & Mazorche, S.R. (2024). Constructive fractional models through Mittag-Leffler functions. Computational and Applied Mathematics, 43(177). https://doi.org/10.1007/s40314-024-02680-z

[31] Agina, P.C., Otugene, V.B., Adedoyin, J.D., Chukwuma, E.I., Chuka-Obidiegwu, B.E., Ezeora, D.I., & Mbah, G.C.E. (2025). Derivation of the basic reproduction number using the next generation matrix for a non-linear Ebola Virus transmission model. International Journal of Mathematical Analysis and Modelling, 8(2), 555–573.

@article{1715457,
      author = {Precious Chikaedum Agina, Victor Bamigwojo Otugene, Doris Ijeoma Ezeora, Kingsley Kelechi Ibeh},
      title = {Modeling Inflation Dynamics with Atangana-Baleanu Fractional Derivatives: A Memory-Driven Approach to Consumer Price Index Forecasting},
      journal = {Iconic Research And Engineering Journals},
      year = {2026},
      volume = {9},
      number = {9},
      pages = {2000-2022},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1715457.pdf},
      abstract = {Inflation dynamics are widely characterized by persistence, delayed adjustment, and pronounced uncertainty, features that are often inadequately captured by conventional integer-order models. This paper develops and applies an Atangana-Baleanu fractional-order inflation framework to analyze Consumer Price Index (CPI) forecast dynamics, with particular emphasis on memory effects, expectation formation, and forecast uncertainty. By incorporating a non-singular kernel and fractional memory, the proposed model allows inflation deviations to decay according to a Mittag-Leffler type process rather than standard exponential adjustment. Using CPI forecast data over multiple horizons, the empirical analysis demonstrates that lower fractional orders are associated with stronger inflation persistence, slower convergence to long-run equilibrium, and sustained forecast dispersion. Comparative evaluation against classical integer-order benchmark models reveals that the fractional framework achieves superior forecasting performance, as reflected in lower error metrics and reduced serial correlation in residuals, especially during periods of elevated macroeconomic uncertainty. The results further suggest that inflation expectations are formed through adaptive and history-dependent mechanisms, with past shocks exerting prolonged influence on both the level and uncertainty of forecasts. On the whole, the findings highlight the economic relevance of the fractional-order parameter as a meaningful measure of inflation inertia and provide strong support for the use of Atangana-Baleanu fractional models in empirical inflation analysis and macroeconomic forecasting.},
      keywords = {Fractional calculus; Atangana-Baleanu derivative; Inflation dynamics; CPI forecasting; Long memory.},
      month = {March},
      doi = {https://doi.org/10.64388/IREV9I9-1715457}
  }