A Stationarity-and-Coupling Criterion for Training-Free Time-Lagged Spectral Embeddings of Multivariate Time Series (opens in new tab)

We study training-free fixed-length descriptors for multivariate time series and ask not merely whether such a descriptor performs well, but when it can be expected to work at all. Our object of study is $D(\tau)$, built from a time-lagged correlation matrix truncated at the Marchenko-Pastur edge so that only signal-bearing eigenvalues survive and classified by cosine similarity to class centroids with zero learned parameters. The central contri...