This paper focuses on activity recognition using a single wearable inertial measurement sensor placed on the subject's chest. The ten activities that need to be identified include lying down, standing, sitting, bending and walking, among others. The activity recognition approach is based on using and identifying a transfer function associated with each activity. The appropriate input and output signals for each transfer function are first determined based on the norms of the sensor signals excited by that specific activity. Then the transfer function is identified using training data and a Wiener filter based on the auto-correlation and cross-correlation of the output and input signals. The activity occurring in real-time is recognized by computing and comparing the input-output errors associated with all the transfer functions. The performance of the developed system is evaluated using data from a group of Parkinson's disease subjects, including data obtained in a clinical setting and data obtained through remote home monitoring. On average, the developed system provides better than 90% accuracy in identifying each activity as it occurs. Activity recognition is particularly useful for PD patients in order to monitor their level of activity, characterize their postural instability and recognize high risk-activities in real-time that could lead to falls.