High-dimensional time series analysis: imputation and testing Kronecker product structure on tensor factor models, main effect factor models, and spatial autoregressive models

Cen, Zetai (2025) High-dimensional time series analysis: imputation and testing Kronecker product structure on tensor factor models, main effect factor models, and spatial autoregressive models. PhD thesis, London School of Economics and Political Science.

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Abstract

High-dimensional time series are increasingly ubiquitous, which leads to an urgent need for statistical methodologies correspondingly. The emergence of tensor time series, where data are arranged as general tensors (e.g. vectors, matrices) at each timestamp, poses new challenges to researchers and practitioners. This thesis sheds light on time series analysis from factor modelling to spatiotemporal analysis. First, we explore how to estimate the factor structure in a tensor factor model with missing data and weak factors. With a rank estimator proposed, we introduce an imputation procedure by leveraging all estimators and discuss how to perform practical inference. We elaborate on the performance of our method with two real data examples on portfolio returns and national economic indicators, respectively. We also attempt to answer a fundamental question on tensor factor modelling: can we test if a factor structure is violated on a given tensor time series while preserved on the flattened series? Generally put, we are interested to understand whether the factor structure is mode-related or not. We formulate the testing problem and provide a residual test with theoretical guarantees, followed by extensive data examples. For matrix time series, we design a factor model with time-varying main effects in addition to a common component to disentangle row and column information of the observed matrix. It assumes a more general structure than the prevalent matrix factor model with Tucker decomposition in the common component governing only the “joint” effect. We establish theories for statistical inference and propose a test on the necessity of our model. We apply our model to study a set of taxi traffic data and discover an “hour” effect within. Lastly, we contribute to the field of spatial econometrics by presenting a spatial autoregressive model with time-varying spatial weights, featuring the spill-over effects among cross-sectional units contemporaneously in the observed vector time series. We circumvent the difficulty of selecting spatial weight matrices by penalised estimation. A set of industrial profits is analysed through our approach.

Item Type:	Thesis (PhD)
Additional Information:	© 2025 Zetai Cen
Library of Congress subject classification:	Q Science > QA Mathematics
Sets:	Departments > Statistics
Supervisor:	Lam, Clifford and Bergsma, Wicher
URI:	http://etheses.lse.ac.uk/id/eprint/4881

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