A2080
Title: Covariate-augmented tensor factor models
Authors: Lingxiao Li - The Hong Kong Polytechnic University (China) [presenting]
Catherine Liu - The Hong Kong Polytechnic University (Hong Kong)
Elynn Chen - New York University (United States)
Abstract: A covariate-augmented CP factor model for high-dimensional tensor-valued time series is studied. The proposed model extends the standard CP factor model by decomposing each mode-specific loading vector into a covariate-relevant component and a covariate-orthogonal component. The covariate effects are modeled nonparametrically through additive sieve approximations, while the residual component allows for latent loading variation not captured by the observed covariates. An iteratively projected CP procedure, IP-SO, is proposed for estimating the loading vectors and latent factors. The method first projects tensor observations onto low-dimensional sieve spaces generated by mode-specific covariates and then applies an iterative simultaneous orthogonalization step to separate the CP components. Convergence rates for the estimated loading structures and latent factors are established under weak temporal dependence. The theory shows that, when the observed covariates are informative about the loadings, the projection step reduces the effective noise dimension and leads to sharper estimation than methods that ignore auxiliary information. Monte Carlo experiments corroborate these findings, showing that IP-SO improves finite sample accuracy in weak signal and high dimensional settings.
