Pronóstico de la demanda estacional en el comercio minorista: exactitud predictiva de SARIMAX frente a Prophet en un panel de tiendas
DOI:
https://doi.org/10.5281/zenodo.22679531Palabras clave:
Pronóstico de demanda, estacionalidad, series temporales, SARIMAX, Prophet, exactitud predictiva, comercio minoristaResumen
Problema. La planificación de inventarios en el comercio minorista depende de pronósticos de demanda que incorporen la estacionalidad anual y los repuntes de calendario, y la elección entre familias de modelos suele resolverse comparando una única serie y un puñado de indicadores de error, sin contraste inferencial que sostenga la preferencia declarada. Objetivo. Comparar la exactitud predictiva de un modelo autorregresivo integrado de media móvil con variables exógenas y estacionalidad armónica (SARIMAX) frente a un modelo aditivo de descomposición con tendencia por tramos (Prophet), sobre un panel de series semanales de venta minorista, y someter la diferencia a contraste estadístico formal. Método. Se analizaron 58 series semanales —29 establecimientos por los dos departamentos de mayor volumen de cada uno— con 143 observaciones consecutivas por serie (2010-02-05 a 2012-10-26), 8 294 observaciones en total. El orden de integración se examinó mediante Dickey-Fuller aumentada y KPSS; SARIMAX se seleccionó por criterio de información corregido a orden de integración fijo y Prophet por validación fuera de muestra interna; la exactitud se evaluó sobre las últimas 13 semanas y mediante validación de origen móvil, y la comparación se sometió a la prueba de Diebold-Mariano con corrección de Harvey-Leybourne-Newbold y a un contraste pareado entre series. Resultados. SARIMAX obtuvo un error de pronóstico menor que Prophet y la diferencia resultó estadísticamente significativa: RMSE medio de 2 247,2 frente a 2 483,8 (diferencia relativa de 9,5 %), t = 3,17, p = 0,002, d_z = 0,416. Serie a serie, el contraste no distingue ambos modelos en 96,6 % de los casos. Conclusión. La preferencia entre familias de modelos de pronóstico no es establecible sobre una serie aislada: exige una unidad de análisis múltiple y una prueba formal sobre la diferencia de pérdida. El procedimiento descrito es replicable sobre cualquier cartera de series de demanda.
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