Physical applications: Analysis of Colombian coffee prices using fractional Brownian motion

Colombia is an exporting country of quality coffee in the world; divergent factors in the short and long term, such as inclement weather, geographic changes, and socio-political development, are some of the factors that influence the price of this product. Knowing the future behavior of this phenomenon is one of the most important studies for economists, academics, coffee growers, entrepreneurs, and exporters. Brownian motion, a physical phenomenon that describes the irregular movement of some particles suspended in a fluid, was described by the probability of finding a particle in a position at a specific time. Fractional Brownian motion describes the random fluctuation of a stochastic process continuous in time and is characterized by the Hurst coefficient to observe persistence and volatility in a time series. The percentage of volatility that changes in the price of coffee present allows generating strategies to maintain the quality of the product and, therefore, its positioning in the market. In this work it was found that the series of data on coffee prices is persistent and that its volatility is 43.77%.