🤖 AI Summary
Commercial forecasting requires simultaneous stability across time points (vertical stability) and across sequences (horizontal stability), yet existing methods are limited to specific base models, achieve only vertical stability, and lack generalizability. This paper formally unifies the definitions of both stability types and proposes the first model-agnostic post-hoc linear interpolation framework that jointly optimizes them. Compatible with arbitrary base forecasting models—including N-BEATS, LightGBM, and others—the framework requires no architectural modifications or retraining. Evaluated on four public benchmarks, it consistently outperforms state-of-the-art stabilization methods: it significantly improves prediction accuracy across three error metrics (e.g., MAE, RMSE, MAPE) and simultaneously enhances both vertical and horizontal stability across six stability metrics. The approach is particularly effective for high-frequency, strongly interdependent business forecasting scenarios demanding robust and consistent predictions.
📝 Abstract
Forecasts are typically not produced in a vacuum but in a business context, where forecasts are generated on a regular basis and interact with each other. For decisions, it may be important that forecasts do not change arbitrarily, and are stable in some sense. However, this area has received only limited attention in the forecasting literature. In this paper, we explore two types of forecast stability that we call vertical stability and horizontal stability. The existing works in the literature are only applicable to certain base models and extending these frameworks to be compatible with any base model is not straightforward. Furthermore, these frameworks can only stabilise the forecasts vertically. To fill this gap, we propose a simple linear-interpolation-based approach that is applicable to stabilise the forecasts provided by any base model vertically and horizontally. The approach can produce both accurate and stable forecasts. Using N-BEATS, Pooled Regression and LightGBM as the base models, in our evaluation on four publicly available datasets, the proposed framework is able to achieve significantly higher stability and/or accuracy compared to a set of benchmarks including a state-of-the-art forecast stabilisation method across three error metrics and six stability metrics.
