On Forecast Stability

TL;DR

This paper addresses forecast stability in rolling-origin forecasting by proposing a simple linear interpolation post-processing framework that stabilizes forecasts vertically and/or horizontally across origins and horizons. The method is model-agnostic and does not require re-fitting base models, enabling explicit control of the stability–accuracy trade-off via a weight parameter. Through extensive experiments on four public datasets using diverse base models, the approach demonstrates significant stability gains and often competitive or improved accuracy, with Pareto-front analyses guiding practical trade-offs. The work offers a practical, extensible baseline for deploying stable forecasts in business settings and suggests avenues for future work on adaptive weighting and integration with decomposition-based stability approaches.

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.

Figures (10)

• Figure 1: Forecasts can be produced from the same or different origins, and for the same or different target. We call the four different possible combinations accordingly: replicability, vertical stability, horizontal stability, vertical and horizontal stability. The blue and green dots respectively represent the origin that the forecasts are made and the target.
• Figure 2: Visualisation of the concepts of vertical and horizontal stability types.
• Figure 3: A visualisation of the increase of vertical stability across series N1402 in the M3 monthly dataset for N-BEATS. Each subplot is corresponding with a different w_s value.
• Figure 4: A visualisation of the increase of vertical stability across the $5^{th}$ series in the Favorita dataset for ETS. Each subplot is corresponding with a different w_s value.
• Figure 5: A visualisation of the increase of horizontal stability across the remainder of series N1403 (origin 1) in the M3 monthly dataset for LightGBM. Each subplot is corresponding with a different w_s value.