Anomaly detection in time series data is a critical challenge across various domains. Traditional methods typically focus on identifying anomalies in immediate subsequent steps, often underestimating the significance of temporal dynamics such as delay time and horizons of anomalies, which generally require extensive post-analysis. This paper introduces a novel approach for detecting time series anomalies called Anomaly Prediction, incorporating temporal information directly into the prediction results. We propose a new dataset specifically designed to evaluate this approach and conduct comprehensive experiments using several state-of-the-art time series forecasting methods. The results demonstrate the efficacy of our approach in providing timely and accurate anomaly predictions, setting a new benchmark for future research in this field.