  Observations in various applications are frequently represented as a time
series of multidimensional arrays, called tensor time series, preserving the
inherent multidimensional structure. In this paper, we present a factor model
approach, in a form similar to tensor CP decomposition, to the analysis of
high-dimensional dynamic tensor time series. As the loading vectors are
uniquely defined but not necessarily orthogonal, it is significantly different
from the existing tensor factor models based on Tucker-type tensor
decomposition. The model structure allows for a set of uncorrelated
one-dimensional latent dynamic factor processes, making it much more convenient
to study the underlying dynamics of the time series. A new high order
projection estimator is proposed for such a factor model, utilizing the special
structure and the idea of the higher order orthogonal iteration procedures
commonly used in Tucker-type tensor factor model and general tensor CP
decomposition procedures. Theoretical investigation provides statistical error
bounds for the proposed methods, which shows the significant advantage of
utilizing the special model structure. Simulation study is conducted to further
demonstrate the finite sample properties of the estimators. Real data
application is used to illustrate the model and its interpretations.
