Fractional Integration Analysis of Rare Earth Material Price Dynamics for Mechanical System Design and Sustainable Manufacturing

Abstract

Rare earth elements (REEs) are strategic resources essential for defense mechanical systems, digital industries, and clean energy technologies. This study examines the persistence and long-term dynamics of REE prices from September 2012 to May 2022 using the ARFIMA mechanical model, which captures both short- and long-memory behavior. Additionally, descriptive statistics and fractional integration analysis are employed to evaluate distributional characteristics and interrelationships among REE prices. The descriptive findings reveal notable heterogeneity across elements, with neodymium, praseodymium, terbium, and dysprosium exhibiting higher mean values, greater volatility, and positive skewness, indicating higher sensitivity to market shocks. The ARFIMA results show that most REE prices are fractionally integrated and mean-reverting, suggesting that shocks are largely transitory. However, neodymium, praseodymium, terbium, and dysprosium display high persistence and near unit-root behavior, implying that shocks may have permanent effects. These findings highlight the importance of critical REEs for supply chain resilience, risk management, and sustainable energy transition policies.