Selecting Data Granularity and Model Specification Using the Scaled Power Likelihood with Multiple Weights

Abstract

Firms routinely employ temporal sales data for making managerial decisions. To use such data appropriately, managers need to make two decisions: (a) the temporal granularity (e.g., weekly, monthly, or quarterly) and (b) an accompanying demand model. In most empirical contexts, however, the “appropriate” granularity-model combination is determined in an ad-hoc manner, leaving managerial decisions vulnerable to granularity and model choices. While extant literature has proposed methods that either select the best-fitted model or conduct robust inference against model misspecification, most methods assume that the granularity is correctly specified or pre-specify it. Our research fills this gap by proposing a method, the scaled power likelihood with multiple weights (SPLM), that not only identifies the best-fitted granularity-model combination but also conducts doubly (granularity and model) robust inference against incorrect selection. An extensive set of simulations shows that our method has higher statistical power than extant approaches for selecting the best-fitted granularity-model combination and provides results that are more stable (robust) across granularity-model combinations. We apply our framework to estimating the price and advertising elasticities for a Nielsen scanner dataset and find that, similar to our simulations, optimal prices and sales forecasts from our approach are more stable across granularity-model combinations.