Automated parameter selection in singular spectrum analysis for time series analysis

In spite of wide applications of the singular spectrum analysis (SSA) method, understanding how SSA reconstructs time series and eliminates noise remains challenging due to its complex process. This study provided a novel geometric perspective to elucidate the underlying mechanism of SSA. To address the key issue of conventional SSA that requires a fixed window length and a given threshold for determining the number of groups, we proposed a sequential reconstruction approach that averages reconstructed series from various window lengths with a stopping rule based on a symmetric test. Three main advantages of the proposed method were demonstrated by the simulations and real data analysis of 7-day heart rate data from an e-cigarette user: (1) requiring no prior knowledge of the window length or group number; (2) yielding smaller values of root mean square error (RMSE) than the conventional SSA; and (3) revealing both local features and sudden changes related to events of interest. While conventional SSA excels in extracting stable signal structures, the proposed method is tailored for time series with varying structures such as heart rate data from smartwatches, and thus will have even wider applications.