Vetting the Extrapolation Caution of Tamhane & Dunlop: A Time Series Forecasting Analysis

Abstract

Context In forecasting there are only two classes of Projections: Extrapolations or Interpolations. Interestingly, Interpolations usually, all but guarantee, that the theoretical expectations that rationalize the veracity of the forecasting profiles are the likely State of Nature. Simply: The [1-a]% Forecasting Prediction Interval [FPI] provides the expected-intel with a frequency of [1-a]%. However, for Extrapolations, [T&D] [8 p. 363] offer the following “Forecasting Bump in the Road” T&D Conjecture: “- - -extrapolation beyond the range of the data is a risky business should be avoided.” If T&D are correct that: Forecasting Extrapolations somehow compromise the linkages of the Projection of the Past into a Relevant Future, Then, indeed, Extrapolations should be avoided. T&D’s theoretical and experientially based caution has garnered very little vetting interest—Voilà: The motivation for our research report. Research Elements Initially, we offer a detailed analysis of the mathematical nature of an Extrapolation as it affects the Precision of the 95% Time Series [TS] Forecasting Prediction Interval [95%TSFPIs]. This is critical as, interestingly, T&D offer no detailed support for their risky business musing. For the inferential testing stage, we will use as the Y-Response Variate: The Capture Rate of the 95%TSFPIs. As we are using a DOE-Inferential Model, we are opting for two-Category Covariates: Extrapolations—[As they are the focus of our inquiry.] & Panel-Variation—measured as the Coefficient of Determination [CoD]—[As variation is the bane of forecasting.]. For DOE: testing, we have selected a random sample of 202 Panels from the S&P₅₀₀; for each Panel there are Three TS-Extrapolations and also Three [CoD-screens]. Results We found clear inferential evidence that as the Extrapolations move away from the mean of the TS time-index & The CoD increases that certain DOE-{Ext & CoD} Tukey-Kramer HSD-interaction-profiles suggest a failure to realizes the theoretical expectations of the Capture Rate of the 95%TSFPIs. We offer, for the first time, a deconstruction of these very interesting inferential DOE-results that rationalize T&D’s risky business musing.