Analysis and prediction of daily physical activity level data using autoregressive integrated moving average models

Results are provided on predicting daily physical activity level (PAL) data from past data of participants of a physical activity lifestyle program aimed at promoting a healthier lifestyle consisting of more physical exercise. The PAL data quantifies the level of a person’s daily physical activity and reflects the daily energy expenditure of this person. In this wellbeing program, a mobile body-worn activity monitor with a built-in triaxial accelerometer was used to record the PAL data of an individual for a period of 13 weeks. The autoregressive integrated moving average (ARIMA) models were employed to predict future PAL data of every next week. This paper proposes a categorized-ARIMA (CARIMA) prediction method which achieves a large reduction in computation time without significant loss in prediction accuracy compared with the traditional ARIMA. In the current method, PAL data were categorized as being stationary, trend or seasonal via assessing their autocorrelation functions. The most appropriate ARIMA model for these three categories was automatically selected by applying the objective penalty function criterion. The results show that our CARIMA method performed well in terms of PAL prediction accuracy (~9% mean absolute percentage error), model parsimony and robustness.