Evolutionary Factor Analysis of Replicated Time Series

Summary In this article, we develop a novel method that explains the dynamic structure of multi‐channel electroencephalograms (EEGs) recorded from several trials in a motor–visual task experiment. Preliminary analyses of our data suggest two statistical challenges. First, the variance at each channel and cross‐covariance between each pair of channels evolve over time. Moreover, the cross‐covariance profiles display a common structure across all pairs, and these features consistently appear across all trials. In the light of these features, we develop a novel evolutionary factor model (EFM) for multi‐channel EEG data that systematically integrates information across replicated trials and allows for smoothly time‐varying factor loadings. The individual EEGs series share common features across trials, thus, suggesting the need to pool information across trials, which motivates the use of the EFM for replicated time series. We explain the common co‐movements of EEG signals through the existence of a small number of common factors. These latent factors are primarily responsible for processing the visual–motor task which, through the loadings, drive the behavior of the signals observed at different channels. The estimation of the time‐varying loadings is based on the spectral decomposition of the estimated time‐varying covariance matrix.