February 2024 Rank and factor loadings estimation in time series tensor factor model by pre-averaging
Weilin Chen, Clifford Lam
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Ann. Statist. 52(1): 364-391 (February 2024). DOI: 10.1214/23-AOS2350


The idiosyncratic components of a tensor time series factor model can exhibit serial correlations, (e.g., finance or economic data), ruling out many state-of-the-art methods that assume white/independent idiosyncratic components. While the traditional higher order orthogonal iteration (HOOI) is proved to be convergent to a set of factor loading matrices, the closeness of them to the true underlying factor loading matrices are in general not established, or only under i.i.d. Gaussian noises. Under the presence of serial and cross-correlations in the idiosyncratic components and time series variables with only bounded fourth-order moments, for tensor time series data with tensor order two or above, we propose a pre-averaging procedure that can be considered a random projection method. The estimated directions corresponding to the strongest factors are then used for projecting the data for a potentially improved re-estimation of the factor loading spaces themselves, with theoretical guarantees and rate of convergence spelt out when not all factors are pervasive. We also propose a new rank estimation method, which utilizes correlation information from the projected data. Extensive simulations are performed and compared to other state-of-the-art or traditional alternatives. A set of tensor-valued NYC taxi data is also analyzed.


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Weilin Chen. Clifford Lam. "Rank and factor loadings estimation in time series tensor factor model by pre-averaging." Ann. Statist. 52 (1) 364 - 391, February 2024. https://doi.org/10.1214/23-AOS2350


Received: 1 July 2023; Revised: 1 October 2023; Published: February 2024
First available in Project Euclid: 7 March 2024

MathSciNet: MR4718419
Digital Object Identifier: 10.1214/23-AOS2350

Primary: 62H12 , 62H25

Keywords: bootstrap tensor fibres , Core rank tensor , iterative projection algorithm , strongest factors projection , tensor fibres pre-averaging

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.52 • No. 1 • February 2024
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