The tensor auto-regressive model

We introduce the tensor auto-regressive (TAR) model for modeling time series data, which is found to be robust to model misspecification, seasonality, and nonlinear trends. We develop a parameter estimation algorithm for the proposed model by using the t-product, which allows us to model a threedimensional block of parameters. We use the fast Fourier transform, which allows for efficient and parallelizable computation. We use a combination of simulated data and an empirical application to: (i) validate the model, including seasonal and geometric trends, model misspecification analysis, and bootstrapping to compute standard errors; (ii) present model selection results; and (iii) demonstrate the performance of the proposed model against benchmarking and competitive forecasting methods. Our results indicate that our model performs well against comparable methods and is robust and computationally efficient.