Abnormal human behavior detection under free-living conditions is a reliable technique to detect activity disorders and diseases. This work proposes an acceleration-based algorithm to detect abnormal behavior as an abnormal increase or decrease in physical activity (PA). The algorithm is based on statistical features of human physical activity. Using a period of observed physical activity as a reference, the algorithm is able to detect abnormal behavior in other periods of time. The approach is unsupervised as the modeling of the reference behavior is not required. It has been validated with a group of 12 users under free-living conditions for two days. Results show a precision greater than 75% and a recall of 92%.