Carvalho-Transformations: A Robustness Analysis in the Forecasting Domain

Abstract

Context Transformations of Panel-data values are routinely made for qualifying datasets with the intention of enhancing the quality of the decision-making-intel that may be gleaned from inferential-testing. Interestingly, there seems to be a “Spill-Over” of this “Conditional Data-Transformation Imperative” that impacts the development and execution of forecasting-protocols.

Focus We offer inferential-tests of Transformations applied to randomly selected S&P₅₀₀ Firm-datasets to address the following research Questions of Interest:

(1) Is there Transformation-Jeopardy if the wrong Box-Cox-Carvalho-Transformations are selected re: (a) The Capture Rate Profiles for the 95% Forecasting Prediction Internals Or (b) The Relative Absolute Forecasting Error [RAFE] for the Forecasting Predictions?

(2) In a consulting context, when Transformations are correctly used, the client almost always requires that the forecasts be re-transformed to the original measure of the data. Is there a Re-Transformation-Jeopardy re: the forecasting decision-intel needed to inform the decision-making processes of the client?

Results We found that the theoretical expectations for the 95% Forecasting Prediction Intervals were founded even if the transforms were not to have been correctly selected. However, if the wrong transformation was to have been selected, non-trivial RAFEs are the likely result. Finally, if the correct transformation was to have been selected, re-Transformations to the original data-measures likely will inform the decision-making processes.