Premium
The tensor auto‐regressive model
Author(s) -
Hill Chelsey,
Li James,
Schneider Matthew J.,
Wells Martin T.
Publication year - 2021
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/for.2735
Subject(s) - computer science , model selection , autoregressive model , parallelizable manifold , computation , bootstrapping (finance) , algorithm , econometrics , mathematics , artificial intelligence
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 ‐product, which allows us to model a three‐dimensional 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.