We present HaPTIC, an approach that infers coherent 4D hand trajectories from monocular videos. Current videobased hand pose reconstruction methods primarily focus on improving frame-wise 3D pose using adjacent frames rather than studying consistent 4D hand trajectories in space. Despite the additional temporal cues, they generally underperform compared to image-based methods due to the scarcity of annotated video data. To address these issues, we repurpose a state-of-the-art image-based transformer to take in multiple frames and directly predict a coherent trajectory. We introduce two types of lightweight attention layers: cross-view self-attention to fuse temporal information, and global cross-attention to bring in larger spatial context. Our method infers 4D hand trajectories similar to the ground truth while maintaining strong 2 D reprojection alignment. We apply the method to both egocentric and allocentric videos. It significantly outperforms existing methods in global trajectory accuracy while being comparable to the state-of-the-art in single-image pose estimation.