A0775
Title: CP factor models of high dimensional tensor time series
Authors: Long Yu - Shanghai University of Finance and Economics (China) [presenting]
Abstract: Factor structure is used to model high-dimensional tensor-variate time series based on CP decomposition. The major target is to exactly identify the factor loadings up to the reflection and permutation indeterminacy. A simple procedure is proposed to estimate the model directly by eigen-analysis with a normalized and truncated auto-cross sample covariance matrix. The asymptotic properties of the proposed estimators are studied under very general conditions, which allow the factor loading vectors to be highly related and the common factors to be correlated. The proposed procedure is adaptive to the sparsity of the factor loading vectors and the strength of the common factors and shows promising performance in a wide range of scenarios. It is also shown how to de-bias the estimator to derive a limiting representation, which will be useful in related inference problems. To further reduce the estimation error, an iterative algorithm based on a novel double projection idea is provided. The improved convergence rate of the iterative estimator is theoretically justified, while the associated de-biasing procedure and limiting distribution are also included. All the results are verified in extensive simulation examples and a real data application.
