Time series analysis over sparse, non-stationary datasets with variational mode decomposition and transfer learning

Abstract

Data volumes have been growing exponentially across many domains. However, in fields such as ecology and environmental monitoring, data remains sparse, creating unique challenges. One such challenge is detecting extreme events (sudden spikes or anomalies in the data) and understanding their causes based on spatiotemporal patterns. The difficulty is exacerbated by time lags between an observed outlier and its underlying trigger, making causal attribution and forecasts difficult. These challenges have implications, particularly for environmental protection and regulatory compliance. This thesis explores the issue of time-series analysis over sparse, non-stationary datasets to support outlier detection and forecasts. We mitigate non-stationarity using variational mode decomposition (VMD) to break the signal into multiple seasonal components. To tackle the challenges of long-term seasonality, we leverage information obtained from the frequency domain regarding dominant lagged relationships within these signals. Finally, we leverage transfer learning to warm-start models at spatial extents where the data are sparse. We validate these ideas in the context of nutrient runoff into surface waters, where identifying and explaining anomalies is critical for the protection of ecosystems. Challenges arise due to three main factors: (1) nutrient time series are naturally non-stationary, which complicates the identification of underlying patterns; (2) temporal models often struggle over an entire season's span; and (3) water quality measurements are often sporadic and sparse. Results showed that the historical similarity mapping of these spatiotemporal profiles and their frequency-motivated seasonality characteristics improved prediction performance in each target series. Additionally, the final proposed model captured more series fluctuations than the base models.