A1188
Title: Tensor double autoregressive model with application to heavy-tailed tensor time series data
Authors: Yuteng Zhang - The University of Hong Kong (China) [presenting]
Ke Zhu - University of Hong Kong (Hong Kong)
Cheng Yu - Univeristy of Chicago (China)
Abstract: Tensor time series are increasingly prevalent in economics and finance, where they often exhibit heavy-tailed distributions alongside time-varying volatilities. However, when tensor time series data have an infinite second moment or exhibit dynamics in both conditional mean and covariance, existing tensor time series models lack a valid statistical inference procedure. A new tensor double autoregressive (TDAR) model is proposed that preserves the tensor structure while jointly capturing the conditional mean and covariance dynamics. The TDAR model is based on a novel constant conditional correlation (CCC) specification, which incorporates a tailored trace-normalization treatment to ensure the identification of the CCC-type tensor model. For the TDAR model, a sufficient condition for its stationarity is provided, the consistency and asymptotic normality of its quasi-maximum likelihood estimator (QMLE) are established, and portmanteau tests are constructed to check its adequacy. Notably, both the QMLE and portmanteau tests are shown to have standard limiting distributions when the tensor time series data have only a finite fractional moment. Hence, the TDAR model has a complete valid statistical inference procedure for dealing with heavy-tailed tensor time series data. Numerical studies via simulations and two real examples demonstrate the practical value of the TDAR model.
