In this paper, we propose a 4-Dimensional Higher-order Local Auto-Correlation (4D HLAC). The method aims to extract the features of a 3D time series, which is regarded as a 4D static pattern. This is an orthodox extension of the original HLAC, which represents correlations among local values in 2D images and can effectively summarize motion in 3D space. To recognize motion in the real world, a recognition system should exploit motion information from the real-world structure. The 4D HLAC feature vector is expected to capture representations for general 3D motion recognition, because the original HLAC performed very well in image recognition tasks. Based on experimental results showing high recognition performance and low computational cost, we conclude that our method has a strong advantage for 3D time series recognition, even in practical situations.