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.

中文翻译：

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用于检测扫描仪数据异常价格变化的协变量相关控制限

目前，消费品的大规模销售数据，称为扫描数据，是通过在零售点的销售点扫描单个产品的条形码来获得的。许多国家统计局使用扫描仪数据来建立消费者价格统计。在此过程中，与其他统计程序一样，检测销售价格中的异常交易是分析的重要步骤。进行此类异常值检测的流行方法是四分位数方法、Hidiroglou-Berthelot 方法、抗性围栏方法和 Tukey 算法。这些方法仅基于有关价格变化的信息，而不基于也可从扫描仪数据中获得的任何其他协变量（例如，销售量或零售店类型）。在本文中，我们提出了一种检测异常价格变化的新方法，该方法考虑了一个额外的协变量，即销量。我们假设价格变化的对数方差是销量的平滑函数，并根据先前观察到的数据估计该函数。我们以数值方式展示了新方法相对于现有方法的优势。我们还将这些方法应用于韩国工商会在 2013 年至 2014 年期间每周收集的真实扫描仪数据，并比较它们的性能。