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The tensor auto‐regressive model

Author

Listed:
  • Chelsey Hill
  • James Li
  • Matthew J. Schneider
  • Martin T. Wells

Abstract

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 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.

Suggested Citation

  • Chelsey Hill & James Li & Matthew J. Schneider & Martin T. Wells, 2021. "The tensor auto‐regressive model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(4), pages 636-652, July.
    • Handle: RePEc:wly:jforec:v:40:y:2021:i:4:p:636-652
    DOI: 10.1002/for.2735
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    References listed on IDEAS

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    1. I. D. Currie & M. Durban & P. H. C. Eilers, 2006. "Generalized linear array models with applications to multidimensional smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 259-280, April.
    2. Gorr, Wilpen L. & Schneider, Matthew J., 2013. "Large-change forecast accuracy: Reanalysis of M3-Competition data using receiver operating characteristic analysis," International Journal of Forecasting, Elsevier, vol. 29(2), pages 274-281.
    3. Koopman, Siem Jan & Ooms, Marius & Carnero, M. Angeles, 2007. "Periodic Seasonal Reg-ARFIMAGARCH Models for Daily Electricity Spot Prices," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 16-27, March.
    4. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521565882.
    5. Kourentzes, Nikolaos & Petropoulos, Fotios & Trapero, Juan R., 2014. "Improving forecasting by estimating time series structural components across multiple frequencies," International Journal of Forecasting, Elsevier, vol. 30(2), pages 291-302.
    6. Flores, Benito E. & Pearce, Stephen L., 2000. "The use of an expert system in the M3 competition," International Journal of Forecasting, Elsevier, vol. 16(4), pages 485-496.
    7. Hua Zhou & Lexin Li & Hongtu Zhu, 2013. "Tensor Regression with Applications in Neuroimaging Data Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 540-552, June.
    8. Koning, Alex J. & Franses, Philip Hans & Hibon, Michele & Stekler, H.O., 2005. "The M3 competition: Statistical tests of the results," International Journal of Forecasting, Elsevier, vol. 21(3), pages 397-409.
    9. Ohlson, Martin & Rauf Ahmad, M. & von Rosen, Dietrich, 2013. "The multilinear normal distribution: Introduction and some basic properties," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 37-47.
    10. Jose, Victor Richmond R. & Winkler, Robert L., 2008. "Simple robust averages of forecasts: Some empirical results," International Journal of Forecasting, Elsevier, vol. 24(1), pages 163-169.
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