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arXiv

PerFeCT-VAR separates shared and personalized VAR dynamics via a cross-client frequency cap and attains the lowest forecast error on multi-store sales data

The work introduces the principle of personalization diversity and PerFeCT-VAR, which decomposes each client's transition matrix into shared low-rank dynamics, shared sparse links, and personalized sparse departures, uses a cross-client frequency cap to derive a sharp shared-personalized identification threshold, and designs Frequency-Capped Thresholding (FCT) for federated estimation; the theory establishes joint linear convergence and statistical rates showing that under sufficient personalization diversity the shared dynamics retain total-sample-size gains while personalized components achieve client-level accuracy; simulations and a multi-store retail revenue application demonstrate predictive and interpretive benefits.