Investigating Temporal Delays in Time-Series Forecasts: Detection and Quantification with the n-Step-Shifting Method

Time-series forecasting is fundamental to decision-making across numerous domains; however, systematic temporal delays in predictions remain a largely overlooked or unrecognised phenomenon. This phenomenon occurs when forecasts regress toward recent observations, resulting in predicted series that closely mirror actual data, but trail behind in time. Such temporal misalignment in predictions has been reported in the literature to undermine model evaluation, method comparison and ranking, and the transferability of forecasting studies, especially in contexts with volatile and irregular time-series patterns. Moreover, prior studies have shown that widely used standard evaluation metrics fail to detect such delays, often leading to misleadingly optimistic assessments of predictive accuracy. Therefore, systematic detection and quantification of such delays in predictions is essential before deploying forecasting models in practice to obtain more reliable, robust, and transferable forecasting practices. To this end, in this study, we make three key contributions through conducted experimental studies using real-world electricity and gas consumption datasets: (i) we demonstrate that temporal delays are not necessarily limited to one time step, contrary to what is often assumed in the literature, and may extend to two or more steps depending on the correlation structure of the underlying data and the choice of input features; (ii) we propose a quantitative n-Step-Shifting (n-SS) method that enables the detection of delays of arbitrary length. This method provides a simple but robust mechanism to identify temporal displacement in forecasts; and (iii) we show that, although they do not directly detect temporal displacement, relative error metrics using a persistence model as baseline have the potential to exhibit a degree of resilience against the deceptive effects of such systematic delays and may provide a basis for the quantification of temporal displacement.