Timely implementation of interventions to slow cognitive decline among older adults requires accurate monitoring to detect changes in cognitive function. Data gathered using wearable devices that can continuously monitor factors known to be associated with cognition could be used to train machine learning models and develop wearable-based cognitive monitoring systems. Using data from over 2,400 older adults in the National Health and Nutrition Examination Survey (NHANES) we developed prediction models to differentiate older adults with normal cognition from those with poor cognition based on outcomes from three cognitive tests measuring different domains of cognitive function. During repeated cross-validation, CatBoost, XGBoost, and Random Forest models performed best when predicting cognition based on processing speed, working memory, and attention (median AUCs >0.82) compared to immediate and delayed recall (median AUCs >0.72) and categorical verbal fluency (median AUC >0.68). Activity and sleep parameters were also more strongly associated with processing speed, working memory, and attention compared to other cognitive subdomains. Our work provides proof of concept that wearable-based cognitive monitoring systems may be a viable alternative to traditional methods for monitoring processing speeds, working memory, and attention. We further identified novel metrics that could be targets in future causal studies seeking to better understand how sleep and activity parameters influence cognitive function among older adults.