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High-dimensional VAR with low-rank transition

Abstract

We propose a vector auto-regressive model with a low-rank constraint on the transition matrix. This model is well suited to predict high-dimensional series that are highly correlated, or that are driven by a small number of hidden factors. While our model has formal similarities with factor models, its structure is more a way to reduce the dimension in order to improve the predictions, rather than a way to define interpretable factors. We provide an estimator for the transition matrix in a very general setting and study its performances in terms of prediction and adaptation to the unknown rank. Our method obtains good result on simulated data, in particular when the rank of the underlying process is small. On macroeconomic data from Giannone et al. (Rev Econ Stat 97(2):436–451, 2015), our method is competitive with state-of-the-art methods in small dimension and even improves on them in high dimension.

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Correspondence to Paul Doukhan.

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P. Alquier: This author gratefully acknowledges financial support from the research programme New Challenges for New Data from LCL and GENES, hosted by the Fondation du Risque and from Labex ECODEC (ANR-11-LABEX-0047). P. Doukhan: The work of the second and the third authors has been developed within the MME-DII center of excellence (ANR-11-LABEX-0023-01) and with the help of PAI-CONICYT MEC \(\hbox {N}^\circ \) 80170072. The authors have been supported by Fondecyt Project 1171335 and Mathamsud 18-MATH-07.

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Alquier, P., Bertin, K., Doukhan, P. et al. High-dimensional VAR with low-rank transition. Stat Comput 30, 1139–1153 (2020). https://doi.org/10.1007/s11222-020-09929-7

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  • DOI: https://doi.org/10.1007/s11222-020-09929-7

Keywords

  • High-dimensional time-series forecasting
  • VAR
  • Low-rank transition matrix
  • Model selection