Abstract The objective of this paper is to show a temporal analysis using autoregressive integrated moving average models of the heavy metal concentration in road sediment and dust of Soacha, a Colombian locality. The representative size fractions in the road sediment and dust were <250 μm and ⩽10 μm, respectively. The results suggest that lead is the best metallic element to study the relationship between the heavy metal concentration in the road sediment and dust (r-Pearson = 0.90). Univariate models (R 2 ⩾ 0.58) suggest that the time series of lead concentrations in road sediment and dust have the same temporal structure. Namely, because they are first-order autoregressive processes, concentrations at a given moment of time are influenced by the immediately preceding concentrations. The transfer function model (R 2 = 0.91) suggests that there is no delay in impulse transfer from road dust concentration to lead concentration in the road sediment. The effect is immediate for a sampling interval of 3 days. The results show that modeling has a better fit during the rainy season compared to the dry season. In the context of the simulation of physical phenomena in engineering, this study is relevant to deepen knowledge in relation to the use of autoregressive integrated moving average models.