Adaptive Sequential Singular Spectrum Analysis: Effective Signal Extraction with Application to Heart Rate Signals Related to E-cigarette Use.

The Singular Spectrum Analysis (SSA) is a useful tool for extracting signals from noisy time series. However, the structural insights provided by SSA are significantly influenced by the choice of window length. While the conventional approach, recommending a larger window length, excels with short to moderately-sized time series, it becomes computationally burdensome for longer time series, potentially amplifying mean squared reconstruction errors. This study addresses this methodological gap by introducing an adaptive sequential SSA method that iteratively selects an optimal window length for efficient extraction of essential eigen-sequences (signals) with minimal reconstruction error. This proposed method is versatile, catering to both short-moderate and lengthy time series. Simulation studies demonstrate its efficacy in scenarios where observed data stem from the sum of two sinusoidal functions and noise. Real data analysis on 6-day heart rate data from a young adult e-cigarette user reveals a distinct clustering of vaping events in the scatter plot of the first and third eigen-sequences, indicating the potential of developing "digital biomarkers" for vaping behavior based on extracted eigen-sequences in future studies. In conclusion, the adaptive sequential SSA method offers a robust and flexible approach for signal extraction in diverse time series applications.