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Macroeconomic forecasting and structural analysis through regularized reduced-rank regression

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Abstract
This paper proposes a strategy to detect and impose reduced-rank restrictions in medium vector autoregressive models. In this framework, it is known that Canonical Correlation Analysis (CCA) does not perform well because inversions of large covariance matrices are required. We propose a method that combines the richness of reduced-rank regression with the simplicity of naive univariate forecasting methods. In particular, we suggest to use a proper shrinkage estimator of the autocovariance matrices that are involved in the computation of CCA, thus obtaining a method that is asymptotically equivalent to CCA, but it is numerically more stable in finite samples. Simulations and empirical applications document the merits of the proposed approach both in forecasting and in structural analysis.

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  • Emmanuela Bernardini & Gianluca Cubadda, 2013. "Macroeconomic forecasting and structural analysis through regularized reduced-rank regression," CEIS Research Paper 289, Tor Vergata University, CEIS, revised 03 Oct 2013.
    • Handle: RePEc:rtv:ceisrp:289
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    Cited by:

    1. Gianluca Cubadda & Alain Hecq, 2021. "Reduced Rank Regression Models in Economics and Finance," CEIS Research Paper 525, Tor Vergata University, CEIS, revised 08 Nov 2021.
    2. Marco Centoni & Gianluca Cubadda, 2015. "Common Feature Analysis of Economic Time Series: An Overview and Recent Developments," CEIS Research Paper 355, Tor Vergata University, CEIS, revised 05 Oct 2015.
    3. 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.
    4. 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.
    5. Horváth, Lajos & Liu, Zhenya & Rice, Gregory & Wang, Shixuan, 2020. "A functional time series analysis of forward curves derived from commodity futures," International Journal of Forecasting, Elsevier, vol. 36(2), pages 646-665.
    6. Gianluca Cubadda & Alain Hecq & Elisa Voisin, 2023. "Detecting Common Bubbles in Multivariate Mixed Causal–Noncausal Models," Econometrics, MDPI, vol. 11(1), pages 1-16, March.
    7. Bartkus Algirdas, 2016. "A New Model with Regime Switching Errors: Forecasting Gdp in Times of Great Recession," Ekonomika (Economics), Sciendo, vol. 95(2), pages 7-29, February.
    8. Gianluca Cubadda & Alain Hecq, 2020. "Dimension Reduction for High Dimensional Vector Autoregressive Models," Papers 2009.03361, arXiv.org, revised Feb 2022.
    9. Smeekes, Stephan & Wijler, Etienne, 2018. "Macroeconomic forecasting using penalized regression methods," International Journal of Forecasting, Elsevier, vol. 34(3), pages 408-430.
    10. 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.
    11. Wan, Runzhe & Li, Yingying & Lu, Wenbin & Song, Rui, 2024. "Mining the factor zoo: Estimation of latent factor models with sufficient proxies," Journal of Econometrics, Elsevier, vol. 239(2).
    12. 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.
    13. Wilms, Ines & Croux, Christophe, 2016. "Forecasting using sparse cointegration," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1256-1267.
    14. Pirschel, Inske & Wolters, Maik H., 2014. "Forecasting German key macroeconomic variables using large dataset methods," Kiel Working Papers 1925, Kiel Institute for the World Economy (IfW Kiel).

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    More about this item

    Keywords

    Reduced rank regression; vector autoregressive models; shrinkage estimation; macroeconomic forecasting.;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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