The Ubiquitous ln-Transformation in Forecasting: It Is More Complicated Than Advertised!

Abstract

Context As Forecasters, we are advised to use the log/ln-Transformation for Y-Variates when there is evidence of a generating process that creates panel-points that are multiplicative over the section of the panel that will be used in developing a Time Series Forecasting Model [TSFM]. This advice is usually given as a Rule—implying that there are no-application-conditions that need to be considered—to wit: If the panel tests to be multiplicative, Then: (i) Apply the ln-Transformation to the Y-Variate-values of the panel, (ii) Select FMs, and (iii) Create the forecasting profiles. We have found in consulting-engagements and, also in academic instruction, that the ln-Transformation merits reflective consideration to arrive at forecasts that inform the decision-making process. Focus In this research report, we offer: A Four-Staged Judgment-Based Decision Analytic Protocol for identifying TSFMs that likely should be included in: {The TSFM Candidate Set} when the ln-Transformation is warranted. These DA-Screening Stages are: (i) Experiential-Based Judgmental Screening where: Decision-Makers evaluate the Relative Absolute Error [RAE] Profiles of the TSFMs as: ln-Transformed & as: Downloaded, (ii) Inferential Screening for the Mean[RAE]s using the Welch[ANOVA]] and their Pairwise Mean[RAE]-comparisons using the Tukey-Kramer HSD-Profiles, (iii) Vetting Screening related to the Median[RAE]s as profiled using the Wilcoxon and Kruskal-Wallis Test and also for their Pairwise Comparisons using the Wilcoxon Method, and (iv) Discovery Screening using a Relational DA:FM-Platform to identify other TSFM-options heretofore not tested that may merit consideration.