Data augmentation with generative adversarial networks (GANs) has been popular for class imbalance problems, mainly for pattern classification and computer vision-related applications. Extreme value forecasting is a challenging field that has various applications from finance to climate change problems. In this study, we present a data augmentation framework for extreme value forecasting. In this framework, our focus is on forecasting extreme values using deep learning models in combination with data augmentation models such as GANs and synthetic minority oversampling technique (SMOTE). We use deep learning models such as convolutional long short-term memory (Conv-LSTM) and bidirectional long short-term memory (BD-LSTM) networks for multistep ahead prediction featuring extremes. We investigate which data augmentation models are the most suitable, taking into account the prediction accuracy overall and at extreme regions, along with computational efficiency. We also present novel strategies for incorporating data augmentation, considering extreme values based on a relevance function. Our results indicate that the SMOTE-based strategy consistently demonstrated superior adaptability, leading to improved performance across both short- and long-horizon forecasts. Conv-LSTM and BD-LSTM exhibit complementary strengths: the former excels in periodic, stable datasets, while the latter performs better in chaotic or non-stationary sequences.