Explainable Artificial Intelligence (XAI) aims at automatically generating explanations that help users scrutinize AI model outputs. While effective XAI methods have been developed for classical AI tasks such as classification, AI-based time series forecasting has so far received little attention. The temporal order and dependencies inherent in time series data make AI-based time series forecasting a unique problem class for XAI. We propose PROTIME, a model-agnostic and probability-based XAI method that determines the importance of past values in time series for AI forecasts. PROTIME explanations highlight the most important values in the time series and their impact on the AI forecasts. We demonstrate the applicability of the novel XAI method based on real-world time series data for AI-based sales forecasting and evaluate its efficacy in a randomized online experiment with 240 participants. Results demonstrate the benefits of PROTIME explanations from users’ perspectives.