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Factor-Augmented VARMA Models With Macroeconomic Applications


  • Jean-Marie Dufour
  • Dalibor Stevanović


We study the relationship between vector autoregressive moving-average (VARMA) and factor representations of a vector stochastic process. We observe that, in general, vector time series and factors cannot both follow finite-order VAR models. Instead, a VAR factor dynamics induces a VARMA process, while a VAR process entails VARMA factors. We propose to combine factor and VARMA modeling by using factor-augmented VARMA (FAVARMA) models. This approach is applied to forecasting key macroeconomic aggregates using large U.S. and Canadian monthly panels. The results show that FAVARMA models yield substantial improvements over standard factor models, including precise representations of the effect and transmission of monetary policy.

Suggested Citation

  • Jean-Marie Dufour & Dalibor Stevanović, 2013. "Factor-Augmented VARMA Models With Macroeconomic Applications," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 491-506, October.
  • Handle: RePEc:taf:jnlbes:v:31:y:2013:i:4:p:491-506
    DOI: 10.1080/07350015.2013.818005

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    References listed on IDEAS

    1. William W. S. Wei, 1978. "Some Consequences of Temporal Aggregation in Seasonal Time Series Models," NBER Chapters, in: Seasonal Analysis of Economic Time Series, pages 433-448, National Bureau of Economic Research, Inc.
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    Cited by:

    1. Nathan Bedock & Dalibor Stevanović, 2017. "An empirical study of credit shock transmission in a small open economy," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 50(2), pages 541-570, May.
    2. Norman R. Swanson & Weiqi Xiong, 2018. "Big data analytics in economics: What have we learned so far, and where should we go from here?," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 51(3), pages 695-746, August.
    3. Maxime Leroux & Rachidi Kotchoni & Dalibor Stevanovic, 2017. "Forecasting economic activity in data-rich environment," EconomiX Working Papers 2017-5, University of Paris Nanterre, EconomiX.
    4. Zongwu Cai & Xiyuan Liu, 2021. "Solving the Price Puzzle Via A Functional Coefficient Factor-Augmented VAR Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202106, University of Kansas, Department of Economics, revised Jan 2021.
    5. Gil-Alana, Luis A. & Gupta, Rangan & Olubusoye, Olusanya E. & Yaya, OlaOluwa S., 2016. "Time series analysis of persistence in crude oil price volatility across bull and bear regimes," Energy, Elsevier, vol. 109(C), pages 29-37.
    6. Helmut Lütkepohl, 2014. "Structural Vector Autoregressive Analysis in a Data Rich Environment: A Survey," Discussion Papers of DIW Berlin 1351, DIW Berlin, German Institute for Economic Research.
    7. Andrea Carriero & Francesco Corsello & Massimiliano Marcellino, 2022. "The global component of inflation volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(4), pages 700-721, June.
    8. Foroni, Claudia & Marcellino, Massimiliano & Stevanović, Dalibor, 2018. "Mixed frequency models with MA components," Working Paper Series 2206, European Central Bank.
    9. Dias, Gustavo Fruet & Kapetanios, George, 2018. "Estimation and forecasting in vector autoregressive moving average models for rich datasets," Journal of Econometrics, Elsevier, vol. 202(1), pages 75-91.
    10. Rachidi Kotchoni & Maxime Leroux & Dalibor Stevanovic, 2019. "Macroeconomic forecast accuracy in a data‐rich environment," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(7), pages 1050-1072, November.
    11. Carriero, Andrea & Kapetanios, George & Marcellino, Massimiliano, 2016. "Structural analysis with Multivariate Autoregressive Index models," Journal of Econometrics, Elsevier, vol. 192(2), pages 332-348.
    12. Joshua C.C. Chan & Eric Eisenstat, 2015. "Efficient estimation of Bayesian VARMAs with time-varying coefficients," CAMA Working Papers 2015-19, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    13. Dalibor Stevanovic, 2015. "Factor augmented autoregressive distributed lag models with macroeconomic applications," CIRANO Working Papers 2015s-33, CIRANO.
    14. Mao Takongmo, Charles Olivier & Stevanovic, Dalibor, 2015. "Selection Of The Number Of Factors In Presence Of Structural Instability: A Monte Carlo Study," L'Actualité Economique, Société Canadienne de Science Economique, vol. 91(1-2), pages 177-233, Mars-Juin.
    15. Monika Bours & Ansgar Steland, 2021. "Large‐sample approximations and change testing for high‐dimensional covariance matrices of multivariate linear time series and factor models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 610-654, June.
    16. Qin Zhang & He Ni & Hao Xu, 2023. "Forecasting models for the Chinese macroeconomy in a data‐rich environment: Evidence from large dimensional approximate factor models with mixed‐frequency data," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 63(1), pages 719-767, March.
    17. Antoine A. Djogbenou, 2024. "Identifying oil price shocks with global, developed, and emerging latent real economy activity factors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(1), pages 128-149, January.

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