A person's physical activity has important health implications, so it is important to be able to measure aspects of physical activity objectively. One approach to doing that is to use data from an accelerometer to classify physical activity according to activity type (e.g., lying down, sitting, standing, or walking) or intensity (e.g., sedentary, light, moderate, or vigorous). This can be formulated as a labeled classification problem, where the model relates a feature vector summarizing the accelerometer signal in a window of time to the activity type or intensity in that window. These data exhibit two key characteristics: (1) the activity classes in different time windows are not independent, and (2) the accelerometer features have moderately high dimension and follow complex distributions. Through a simulation study and applications to three datasets, we demonstrate that a model's classification performance is related to how it addresses these aspects of the data. Dynamic methods that account for temporal dependence achieve better performance than static methods that do not. Generative methods that explicitly model the distribution of the accelerometer signal features do not perform as well as methods that take a discriminative approach to establishing the relationship between the accelerometer signal and the activity class. Specifically, Conditional Random Fields consistently have better performance than commonly employed methods that ignore temporal dependence or attempt to model the accelerometer features.