We propose an approach to estimate arm and hand dynamics from monocular video by utilizing the relationship between arm and hand. Although monocular full human motion capture technologies have made great progress in recent years, recovering accurate and plausible arm twists and hand gestures from in-the-wild videos still remains a challenge. To solve this problem, our solution is proposed based on the fact that arm poses and hand gestures are highly correlated in most real situations. To fully exploit arm-hand correlation as well as inter-frame information, we carefully design a Spatial-Temporal Parallel Arm-Hand Motion Transformer (PAHMT) to predict the arm and hand dynamics simultaneously. We also introduce new losses to encourage the estimations to be smooth and accurate. Besides, we collect a motion capture dataset including 200K frames of hand gestures and use this data to train our model. By integrating a 2D hand pose estimation model and a 3D human pose estimation model, the proposed method can produce plausible arm and hand dynamics from monocular video. Extensive evaluations demonstrate that the proposed method has advantages over previous state-of-the-art approaches and shows robustness under various challenging scenarios.