This paper contains an empirical bid - ask spread analysis. The serial covariance of price changes is compared with the respective bid - ask spread which is explained by the inventory control effect. The underlying assumption is that, in an efficient market with a constant bid - ask spread over a certain period of time, any change in the price can only be due to the spread. We analyse empirically the relationship between the serial covariance of returns calculated from daily and weekly price quotes and the square of quoted spreads. The results indicate a positive relationship between the covariance of price changes and the spread based on the daily data which is in contradiction to the inventory control argument which calls for a negative relationship. Based on weekly data, we get a tendency towards a negative relationship between the covariance of price changes and the spread which seems to confirm the inventory control effect.