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Reduced-Rank Matrix Autoregressive Models: A Medium $N$ Approach

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  • Alain Hecq
  • Ivan Ricardo
  • Ines Wilms

Abstract

Reduced-rank regressions are powerful tools used to identify co-movements within economic time series. However, this task becomes challenging when we observe matrix-valued time series, where each dimension may have a different co-movement structure. We propose reduced-rank regressions with a tensor structure for the coefficient matrix to provide new insights into co-movements within and between the dimensions of matrix-valued time series. Moreover, we relate the co-movement structures to two commonly used reduced-rank models, namely the serial correlation common feature and the index model. Two empirical applications involving U.S.\ states and economic indicators for the Eurozone and North American countries illustrate how our new tools identify co-movements.

Suggested Citation

  • Alain Hecq & Ivan Ricardo & Ines Wilms, 2024. "Reduced-Rank Matrix Autoregressive Models: A Medium $N$ Approach," Papers 2407.07973, arXiv.org.
  • Handle: RePEc:arx:papers:2407.07973
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    References listed on IDEAS

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    1. Cubadda, Gianluca & Guardabascio, Barbara & Hecq, Alain, 2017. "A vector heterogeneous autoregressive index model for realized volatility measures," International Journal of Forecasting, Elsevier, vol. 33(2), pages 337-344.
    2. Vahid, F & Engle, Robert F, 1993. "Common Trends and Common Cycles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 341-360, Oct.-Dec..
    3. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1113-1141, December.
    4. Monica Billio & Roberto Casarin & Matteo Iacopini & Sylvia Kaufmann, 2023. "Bayesian Dynamic Tensor Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(2), pages 429-439, April.
    5. Gianluca Cubadda & Alain Hecq, 2022. "Dimension Reduction for High‐Dimensional Vector Autoregressive Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(5), pages 1123-1152, October.
    6. Elynn Y. Chen & Jianqing Fan, 2023. "Statistical Inference for High-Dimensional Matrix-Variate Factor Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(542), pages 1038-1055, April.
    7. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    8. Kock, Anders Bredahl & Callot, Laurent, 2015. "Oracle inequalities for high dimensional vector autoregressions," Journal of Econometrics, Elsevier, vol. 186(2), pages 325-344.
    9. Cubadda, Gianluca & Guardabascio, Barbara, 2019. "Representation, estimation and forecasting of the multivariate index-augmented autoregressive model," International Journal of Forecasting, Elsevier, vol. 35(1), pages 67-79.
    10. Cubadda, Gianluca & Hecq, Alain & Palm, Franz C., 2009. "Studying co-movements in large multivariate data prior to multivariate modelling," Journal of Econometrics, Elsevier, vol. 148(1), pages 25-35, January.
    11. Connor, Gregory & Korajczyk, Robert A, 1993. "A Test for the Number of Factors in an Approximate Factor Model," Journal of Finance, American Finance Association, vol. 48(4), pages 1263-1291, September.
    12. Wang, Di & Zheng, Yao & Li, Guodong, 2024. "High-dimensional low-rank tensor autoregressive time series modeling," Journal of Econometrics, Elsevier, vol. 238(1).
    13. Diebold, Francis X. & Yilmaz, Kamil, 2015. "Financial and Macroeconomic Connectedness: A Network Approach to Measurement and Monitoring," OUP Catalogue, Oxford University Press, number 9780199338306.
    14. Alain Hecq & Franz C. Palm & Jean‐Pierre Urbain, 2000. "Permanent‐transitory Decomposition in Var Models With Cointegration and Common Cycles," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 62(4), pages 511-532, September.
    15. Carriero, Andrea & Kapetanios, George & Marcellino, Massimiliano, 2016. "Structural analysis with Multivariate Autoregressive Index models," Journal of Econometrics, Elsevier, vol. 192(2), pages 332-348.
    16. Rong Chen & Dan Yang & Cun-Hui Zhang, 2022. "Factor Models for High-Dimensional Tensor Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(537), pages 94-116, January.
    17. repec:bla:obuest:v:62:y:2000:i:4:p:511-32 is not listed on IDEAS
    18. Wang, Dong & Liu, Xialu & Chen, Rong, 2019. "Factor models for matrix-valued high-dimensional time series," Journal of Econometrics, Elsevier, vol. 208(1), pages 231-248.
    19. Gianluca Cubadda & Alain Hecq, 2020. "Dimension Reduction for High Dimensional Vector Autoregressive Models," Papers 2009.03361, arXiv.org, revised Feb 2022.
    20. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 369-380, October.
    21. S. Yaser Samadi & Wiranthe B. Herath, 2023. "Reduced-rank Envelope Vector Autoregressive Models," Papers 2309.12902, arXiv.org.
    22. Elynn Y. Chen & Ruey S. Tsay & Rong Chen, 2020. "Constrained Factor Models for High-Dimensional Matrix-Variate Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(530), pages 775-793, April.
    23. Ledyard Tucker, 1966. "Some mathematical notes on three-mode factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 279-311, September.
    24. Di Wang & Yao Zheng & Heng Lian & Guodong Li, 2022. "High-Dimensional Vector Autoregressive Time Series Modeling via Tensor Decomposition," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(539), pages 1338-1356, September.
    25. James H. Stock & Mark W. Watson, 1989. "New Indexes of Coincident and Leading Economic Indicators," NBER Chapters, in: NBER Macroeconomics Annual 1989, Volume 4, pages 351-409, National Bureau of Economic Research, Inc.
    26. Chen, Rong & Xiao, Han & Yang, Dan, 2021. "Autoregressive models for matrix-valued time series," Journal of Econometrics, Elsevier, vol. 222(1), pages 539-560.
    27. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 393-395, October.
    28. Gianluca Cubadda & Marco Mazzali, 2024. "The vector error correction index model: representation, estimation and identification," The Econometrics Journal, Royal Economic Society, vol. 27(1), pages 126-150.
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