SMU SOE Seminar Series (March 27, 2026): CP-factorization for High Dimensional Tensor Time Series and Double Projection Iterations

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ABSTRACT

We adopt the canonical polyadic (CP) decomposition to model high-dimensional tensor time series. Our primary goal is to identify and estimate the factor loadings in the CP decomposition. We propose a one-pass estimation procedure through standard eigen-analysis for a matrix constructed based on the serial dependence structure of the data. The asymptotic properties of the proposed estimator are established under a general setting as long as the factor loading vectors are algebraically linear independent, allowing the factors to be correlated and the factor loading vectors to be not nearly orthogonal. The procedure adapts to the sparsity of the factor loading vectors, accommodates weak factors, and demonstrates strong performance across a wide range of scenarios. A tractable limiting representation of the estimator is derived, which plays a key role in the related inference problems. To further reduce estimation errors, we also introduce an iterative algorithm based on a novel double projection approach. We theoretically justify the improved convergence rate of the iterative estimator, and also provide the associated limiting distribution. All results are validated through extensive simulations and a real data application.