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

• Author(s): Precious Chikaedum Agina; Victor Bamigwojo Otugene; Doris Ijeoma Ezeora; Kingsley Kelechi Ibeh
• Paper ID: 1715457
• Page: 2000-2022
• Published Date: 24-03-2026
• Published In: Iconic Research And Engineering Journals
• Publisher: IRE Journals
• e-ISSN: 2456-8880
• Volume/Issue: Volume 9 Issue 9 March-2026

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.

Citations

IRE Journals:
Precious Chikaedum Agina, Victor Bamigwojo Otugene, Doris Ijeoma Ezeora, Kingsley Kelechi Ibeh "Modeling Inflation Dynamics with Atangana-Baleanu Fractional Derivatives: A Memory-Driven Approach to Consumer Price Index Forecasting" Iconic Research And Engineering Journals Volume 9 Issue 9 2026 Page 2000-2022 https://doi.org/10.64388/IREV9I9-1715457

IEEE:
Precious Chikaedum Agina, Victor Bamigwojo Otugene, Doris Ijeoma Ezeora, Kingsley Kelechi Ibeh "Modeling Inflation Dynamics with Atangana-Baleanu Fractional Derivatives: A Memory-Driven Approach to Consumer Price Index Forecasting" Iconic Research And Engineering Journals, 9(9) https://doi.org/10.64388/IREV9I9-1715457