With the recent development and popularity of wearable devices, accelerometer data have been increasingly collected to measure physical activity. An accelerometer monitors acceleration in one or more directions, and the signals can then be translated into intensity and duration of physical activities as well as daily activity patterns. While accelerometer data contain rich information on physical activity, statistical methods to effectively extract the information are still lacking. Motivated by a toddler Actiwatch dataset from the Shanghai Children's Medical Center in China, I will discuss our proposed methods to analyze accelerometer data, from daily activity patterns, time shifts to periodicity. More specifically, we propose to use functional Principal Component Analysis to characterize daily activity patterns and variations across individuals; functional registration to align activity curves and infer morning and night individuals; Fast Fourier Transform to detect periodicity and describe circadian rhythms. Results from the toddler Actiwatch dataset analyzed with our methods suggest that the formation of circadian rhythm is associated with early childhood physical development.