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Detection of rare objects (e.g., traffic cones, traffic barrels and traffic warning triangles) is an important perception task to improve the safety of autonomous driving. Training of such models typically requires a large number of annotated data which is expensive and time consuming to obtain. To address the above problem, an emerging approach is to apply data augmentation to automatically generate cost-free training samples. In this work, we propose a systematic study on simple Copy-Paste data augmentation for rare object detection in autonomous driving. Specifically, local adaptive instance-level image transformation is introduced to generate realistic rare object masks from source domain to the target domain. Moreover, traffic scene context is utilized to guide the placement of masks of rare objects. To this end, our data augmentation generates training data with high quality and realistic characteristics by leveraging both local and global consistency. In addition, we build a new dataset, Rare Object Dataset (ROD), consisting 10k training images, 4k validation images and the corresponding labels with a diverse range of scenarios in autonomous driving. Experiments on ROD show that our method achieves promising results on rare object detection. We also present a thorough study to illustrate the effectiveness of our local-adaptive and global constraints based Copy-Paste data augmentation for rare object detection. The data, development kit and more information of ROD are available online at: \url{https://nullmax-vision.github.io}.