Journal
JOURNAL OF ECONOMETRICS
Volume 238, Issue 1, Pages -Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.jeconom.2023.105544
Keywords
global trade flows; high-dimensional time series; non-convex tensor regression; nuclear norm; tensor decomposition; tensor-valued time series
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This paper proposes a new modeling framework for modeling and forecasting high-dimensional tensor-valued time series using the autoregression method. By considering a low-rank Tucker decomposition, this method can flexibly capture the underlying low-dimensional tensor dynamics, achieving dimension reduction and multidimensional dynamic factor interpretations. The paper also studies different estimation methods and their non-asymptotic properties under different low-rank settings.
Modern technological advances have enabled an unprecedented amount of structured data with complex temporal dependence, urging the need for new methods to efficiently model and forecast high-dimensional tensor-valued time series. This paper provides a new modeling framework to accomplish this task via autoregression (AR). By considering a low-rank Tucker decomposition for the transition tensor, the proposed tensor AR can flexibly capture the underlying low-dimensional tensor dynamics, providing both substantial dimension reduction and meaningful multidimensional dynamic factor interpretations. For this model, we first study several nuclearnorm-regularized estimation methods and derive their non-asymptotic properties under the approximate low-rank setting. In particular, by leveraging the special balanced structure of the transition tensor, a novel convex regularization approach based on the sum of nuclear norms of square matricizations is proposed to efficiently encourage low-rankness of the coefficient tensor. To further improve the estimation efficiency under exact low-rankness, a non-convex estimator is proposed with a gradient descent algorithm, and its computational and statistical convergence guarantees are established. Simulation studies and an empirical analysis of tensor-valued time series data from multi-category import-export networks demonstrate the advantages of the proposed approach.
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