Mild cognitive impairment (MCI) is the precursor to the advanced stage of Alzheimer’s disease (AD), and it is important to detect the transition to the MCI condition as early as possible. Trends in daily routines/activities provide a measurement of cognitive/functional status, particularly in older adults. In this study, activity data from longitudinal monitoring through in-home ambient sensors are leveraged in predicting the transition to the MCI stage at a future time point. The activity dataset from the Oregon Center for Aging and Technology (ORCATECH) includes measures representing various domains such as walk, sleep, etc. Each sensor-captured activity measure is constructed as a time series, and a variety of summary statistics is computed. The similarity between one individual’s activity time series and that of the remaining individuals is also computed as distance measures. The long short-term memory (LSTM) recurrent neural network is trained with time series statistics and distance measures for the prediction modeling, and performance is evaluated by classification accuracy. The model outcomes are explained using the SHapley Additive exPlanations (SHAP) framework. LSTM model trained using the time series statistics and distance measures outperforms other modeling scenarios, including baseline classifiers, with an overall prediction accuracy of 83.84%. SHAP values reveal that sleep-related features contribute the most to the prediction of the cognitive stage at the future time point, and this aligns with the findings in the literature. Findings from this study not only demonstrate that a practical, less expensive, longitudinal monitoring of older adults’ activity routines can benefit immensely in modeling AD progression but also unveil the most contributing features that are medically applicable and meaningful.