Estimating the signal dimension in multivariate time series using augmented second order source separation methods

Modeling multivariate time series becomes increasingly challenging as the number of variables grows or when temporal dependencies exhibit high complexity. Within the framework of an internal noise model, it is assumed that the observed time series can be decomposed into two latent components: a signal series and a noise series. In this study, we propose and evaluate an augmentation-based estimator for determining the signal dimension, leveraging the second-order blind identification estimator. The estimator’s performance is assessed across various noise and signal scenarios through an extensive simulation study, providing insights into its practical utility in complex time series analysis.