The bullwhip effect (BE) consists of the demand variability amplification that exists in a supply chain when moving upwards. This undesirable effect produces excess inventory and poor customer service. Recently, several research papers from either a theoretical or empirical point of view have indicated the nature of the de- mand process as a key aspect to defining the BE. Nonetheless, they reached different conclusions. On the one hand, theoretical research quantified the BE depending on the lead time and ARIMA parameters, where ARIMA functions were employed to model the demand generator process. In turn, empirical research related nonlinearly the demand variability extent with the BE size. Although, it seems that both results are contradictory, this paper explores how those conclusions complement each other. Essentially, it is shown that the theoretical developments are precise to determine the presence of the BE based on its ARIMA parameter estimates. Nonetheless, to quan- tify the size of the BE, the demand coefficient of variation should be incorporated. The analysis explores a two-staged serially linked supply chain, where weekly data at SKU level from a manufacturer specialized in household products and a major UK grocery retailer have been collected.