TENSOR REGRESSION AND TENSOR TIME SERIES ANALYSES FOR HIGH DIMENSIONAL DATA

Many real data are naturally represented as a multidimensional array called a tensor. In classical regression and time series models, the predictors and covariate variables are considered as a vector. However, due to high dimensionality of predictor variables, these types of models are inefficient for analyzing multidimensional data. In contrast, tensor structured models use predictors and covariate variables in a tensor format. Tensor regression and tensor time series models can reduce high dimensional data to a low dimensional framework and lead to efficient estimation and prediction. In this thesis, we discuss the modeling and estimation procedures for both tensor regression models and tensor time series models. The results of simulation studies and a numerical analysis are provided