Modeling the conditional volatility of arabica coffee prices

Abstract

Arabica coffee (Coffea arabica) accounts for more than 60% of the world’s coffee production. It is valued for its aromatic complexity and sweet flavor. This work aims to model the volatility of Arabica coffee prices and fit a model to estimate their variations. The data covers monthly prices per 60 kg bag from January 1995 to December 2023. Initially, the price series was transformed into the series of logarithmic returns. The AR(1) model with a cosine component was used to model the existing periodicity and residual autocorrelation. However, the Box-Pierce test, applied to the series of squared residuals, still indicated heteroscedasticity. Therefore, a GARCH(1,1) model with a Skew t-Student distribution for the residuals was fitted. This model was chosen due to the lowest AIC (Akaike Information Criterion) value. It was also found that the residuals of the GARCH(1,1) model can be considered white noise. The interval projection for conditional volatility indicated that coffee prices over the next six months could fall by up to 12% or rise by up to 14%, approximately.