  Currently, large-scale sales data for consumer goods, called scanner data,
are obtained by scanning the bar codes of individual products at the points of
sale of retail outlets. Many national statistical offices use scanner data to
build consumer price statistics. In this process, as in other statistical
procedures, the detection of abnormal transactions in sales prices is an
important step in the analysis. Popular methods for conducting such outlier
detection are the quartile method, the Hidiroglou-Berthelot method, the
resistant fences method, and the Tukey algorithm. These methods are based
solely on information about price changes and not on any of the other
covariates (e.g., sales volume or types of retail shops) that are also
available from scanner data. In this paper, we propose a new method to detect
abnormal price changes that takes into account an additional covariate, namely,
sales volume. We assume that the variance of the log of the price change is a
smooth function of the sales volume and estimate the function from previously
observed data. We numerically show the advantages of the new method over
existing methods. We also apply the methods to real scanner data collected at
weekly intervals by the Korean Chamber of Commerce and Industry between 2013
and 2014 and compare their performance.
