Matching correlated VAR time series
Researchers have developed a new method for matching correlated Vector Autoregressive (VAR) time series databases. The approach introduces a probabilistic framework to recover hidden permutations between two time series, generalizing the problem of matching point clouds to time series. The study derives a maximum likelihood estimator (MLE) and analyzes an estimator based on linear assignment, providing recovery guarantees based on noise thresholds. Additionally, the paper proposes using convex relaxations of permutation matrices, such as the Birkhoff polytope, to efficiently estimate parameters via alternating minimization, with empirical results showing linear assignment often performs comparably or better than MLE relaxation methods. AI