A0988
Title: On testing Kronecker product structure in tensor factor models
Authors: Zetai Cen - University of Bristol (United Kingdom) [presenting]
Clifford Lam - London School of Economics and Political Science (United Kingdom)
Abstract: The aim is to propose a test for testing the Kronecker product structure of a factor loading matrix implied by a tensor factor model with Tucker decomposition in the common component. By defining a Kronecker product structure set, it is determined whether a tensor time series has a Kronecker product structure, which is equivalent to the ability to decompose the series according to a tensor factor model. The test is built on analyzing and comparing the residuals from fitting a full tensor factor model and the residuals from fitting a factor model on a reshaped version of the data. In the most extreme case, the reshaping is the vectorization of the tensor data, and the factor loading matrix in such a case can be general if there is no Kronecker product structure present. Theoretical results are developed through asymptotic normality results on estimated residuals. Numerical experiments suggest that the size of the tests gets closer to the pre-set nominal value as the sample size or the order of the tensor gets larger, while the power increases with mode dimensions and the number of combined modes. Out-tests are demonstrated through New York City taxi traffic data and a Fama-French matrix portfolio of returns.
