Forecasting Commodity Prices with Memory: An Application of Approximate Arithmetic Fractional Brownian Motion to Pet Markets

This study explores the use of fractional Brownian motion (fBm) and its approximation in modeling polyethylene terephthalate (PET) prices. We compare the performance of the Arithmetic Brownian Motion (ABM) model with the approximate arithmetic fractional Brownian motion (AAFBM) model, which accounts for long-range dependencies in price data. Using PET price data from 2018 to 2021, our results show that the AAFBM model outperforms the ABM model, offering improved forecasting accuracy. This approach provides valuable insights for commodity price forecasting and risk management. 2020 Mathematics Subject Classification. 60G22; 91B84; 62M10; 91G60. Key words and phrases. fractional brownian motion; price modeling; commodity forecasting; PET.