Missing data imputation for wearable time series

Abstract

Continuous physiological monitoring via wearables enables early disease detection, diagnosis, and treatment. However, accurate estimation of missing data is essential. Wearable-derived physiological signals often have periodic structure in observations, while the missingness mechanism may follow distinct patterns. Most imputation methods ignore these underlying cycles. We introduce a Periodic Multi-scale Imputation (PMSI) framework to impute missing data, modeling multi-scale periodic dependencies for both observations and missingness patterns. The process follows three stages: (1) identify candidate periodicities; (2) transform series into multi-dimensional tensors aligned with selected periodicities; (3) optimize hyperparameters using a two-layer minimization of Akaike information criterion. PMSI first models the missingness mechanism and generates synthetic masks for optimization, and then estimates missing values using periodicities. We validated PMSI using a smartwatch-derived heart rate dataset, consisting of 558 participant-month series in a high-adherence cohort and 1,957 in a low-adherence cohort. Spectral analysis revealed daily and 3.5-day (likely smartwatch charging) periodicities in the missingness mechanism, and daily and weekly periodicities in observations. The optimal PMSI algorithm used hourly resolution and daily periodicity, and outperformed five standard imputation methods: k-nearest neighbors, autoregressive integrated moving average, convolutional neural networks, piecewise linear interpolation, and last observation carried forward. PMSI performed the best: RMSE (7.53 vs. 8.18–10.01) and MAE (6.04 vs. 6.60–8.16) in the high-adherence cohort, and RMSE (8.81 vs. 9.02–15.86) and MAE (6.60 vs. 6.96–12.44) in the low-adherence cohort (all adjusted p < 0.05). PMSI improves imputation accuracy by modeling periodic dependencies and has broad potential applications for health-related time series.