Using analytic geometry to quantify the period-to-period changes in an array of values

Abstract

Purpose This paper develops a vector variation score that quantifies the change in an array of data points from period-to-period. The array could be the amounts reported on an income tax return, the closing stock prices for a set of listed companies, the monthly sales amounts for retail locations or the monthly balances in general ledger accounts. Design/methodology/approach The score is grounded in analytic geometry. The angle θ measures whether the changes were uniformly spread across the line items. The item(s) with the largest contribution(s) to the score can be identified. Line items can be weighted such that they contribute less than fully to the score. Findings The method can identify tax returns with large year-on-year changes. The method can identify the fact that the price movements during earnings season are less dependent than is usually the case. The method can identify anomalies in reported sales amounts. The method should be able to identify ledger accounts’ large abnormal changes. Research limitations/implications Auditors will need to be trained to interpret the results and to reduce the number of false positives. Practical implications The score could be used in both external and internal audit applications where auditors want to quantify and rank period-on-period changes in a search for outliers. Originality/value The change score is normalized to the [0, 1] range. The results can be plotted as a polar plot for display on an auditing dashboard. The contribution of a single line item can be calculated and line items can be weighted to prevent them from having an undue influence on the results.