The periodic transport of sand mists over the Atlantic towards the arc of the Lesser Antilles is the major particulate pollution factor in the Caribbean area. Given the impact of desert dust on human health and the climate, it is necessary to model and predict the fluctuations in the concentrations of particles with a diameter less than or equal to 10 µm (PM10). For this purpose, the coupled model SARIMA-GARCH (Seasonal Autoregressive Integrated Moving Average and Generalized Autoregressive Conditional Heteroscedastic) was developed. The SARIMA method is representative of the main sources of PM10, while heteroscedasticity (non-normality of SARIMA residues) is also taken into account by the GARCH method. To carry out this work, the PM10 data from Guadeloupe and Puerto Rico were broken down into the sum of several components: the background atmosphere (anthropogenic activities + marine aerosols), the seasonality of desert dust (mineral dust) and the events extremes. The various performance indicators used validated the forecasts of the SARIMA-GARCH model. Thus, the SARIMA-GARCH combination is an effective tool for predicting the behavior of PM10 in the Caribbean zone.