Remote Work in Latin America: Lessons Learned from the Private and Public Sectors

Abstract

Problem. Inventory planning in retail depends on demand forecasts that incorporate annual seasonality and calendar spikes, and the choice between model families is often settled by comparing a single series and a handful of error indicators, without formal inferential contrast supporting the stated preference. Objective. To compare the predictive accuracy of a seasonal autoregressive integrated moving average model with exogenous regressors and harmonic seasonality (SARIMAX) against an additive decomposition model with piecewise trend (Prophet), across a panel of weekly retail sales series, and to subject the difference to formal statistical testing. Method. Fifty-eight weekly series were analyzed—29 stores across the two highest-volume departments of each—with 143 consecutive observations per series (2010-02-05 to 2012-10-26), totaling 8,294 observations. The order of integration was assessed with augmented Dickey-Fuller and KPSS tests; SARIMAX was selected via a corrected information criterion at a fixed integration order, and Prophet via internal out-of-sample validation; accuracy was evaluated on the last 13 weeks and through rolling-origin validation, and the comparison was subjected to the Diebold-Mariano test with the Harvey-Leybourne-Newbold small-sample correction and a paired contrast across series. Results. SARIMAX achieved lower forecast error than Prophet, and the difference was statistically significant: mean RMSE of 2,247.2 versus 2,483.8 (9.5% relative difference), t = 3.17, p = .002, d_z = 0.416. Series by series, the test failed to distinguish the two models in 96.6% of cases. Conclusion. Preference between forecasting model families cannot be established on a single series: it requires a multiple analysis unit and a formal test on the loss differential. The described procedure is replicable across any demand-series portfolio.