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Large Vector Auto Regressions

Author

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  • Song Song
  • Peter J. Bickel

Abstract

One popular approach for nonstructural economic and financial forecasting is to include a large number of economic and financial variables, which has been shown to lead to significant improvements for forecasting, for example, by the dynamic factor models. A challenging issue is to determine which variables and (their) lags are relevant, especially when there is a mixture of serial correlation (temporal dynamics), high dimensional (spatial) dependence structure and moderate sample size (relative to dimensionality and lags). To this end, an integrated solution that addresses these three challenges simultaneously is appealing. We study the large vector auto regressions here with three types of estimates. We treat each variable's own lags different from other variables' lags, distinguish various lags over time, and is able to select the variables and lags simultaneously. We first show the consequences of using Lasso type estimate directly for time series without considering the temporal dependence. In contrast, our proposed method can still produce an estimate as efficient as an oracle under such scenarios. The tuning parameters are chosen via a data driven "rolling scheme" method to optimize the forecasting performance. A macroeconomic and financial forecasting problem is considered to illustrate its superiority over existing estimators.

Suggested Citation

  • Song Song & Peter J. Bickel, 2011. "Large Vector Auto Regressions," SFB 649 Discussion Papers SFB649DP2011-048, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2011-048
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    Citations

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    Cited by:

    1. Chang, Jinyuan & Guo, Bin & Yao, Qiwei, 2015. "High dimensional stochastic regression with latent factors, endogeneity and nonlinearity," LSE Research Online Documents on Economics 61886, London School of Economics and Political Science, LSE Library.
    2. Jorge A Chan-Lau, 2017. "Lasso Regressions and Forecasting Models in Applied Stress Testing," IMF Working Papers 17/108, International Monetary Fund.
    3. Fengler, Matthias R. & Gisler, Katja I.M., 2015. "A variance spillover analysis without covariances: What do we miss?," Journal of International Money and Finance, Elsevier, vol. 51(C), pages 174-195.
    4. Song, Song & Zhu, Lixing, 2016. "Group-wise semiparametric modeling: A SCSE approach," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 1-14.
    5. Li, Jiahan & Chen, Weiye, 2014. "Forecasting macroeconomic time series: LASSO-based approaches and their forecast combinations with dynamic factor models," International Journal of Forecasting, Elsevier, vol. 30(4), pages 996-1015.
    6. Kock, Anders Bredahl & Callot, Laurent, 2015. "Oracle inequalities for high dimensional vector autoregressions," Journal of Econometrics, Elsevier, vol. 186(2), pages 325-344.
    7. Song Song & Wolfgang K. Härdle & Ya'acov Ritov, 2014. "Generalized dynamic semi‐parametric factor models for high‐dimensional non‐stationary time series," Econometrics Journal, Royal Economic Society, vol. 17(2), pages 101-131, June.
    8. Daniel Felix Ahelegbey & Monica Billio & Roberto Casarin, 2016. "Sparse Graphical Vector Autoregression: A Bayesian Approach," Annals of Economics and Statistics, GENES, issue 123-124, pages 333-361.
    9. Jorge A Chan-Lau, 2017. "Variance Decomposition Networks; Potential Pitfalls and a Simple Solution," IMF Working Papers 17/107, International Monetary Fund.
    10. repec:eee:intfor:v:33:y:2017:i:3:p:627-651 is not listed on IDEAS
    11. Song Song, 2011. "Dynamic Large Spatial Covariance Matrix Estimation in Application to Semiparametric Model Construction via Variable Clustering: the SCE approach," Papers 1106.3921, arXiv.org, revised Jun 2011.
    12. Kascha, Christian & Trenkler, Carsten, 2015. "Forecasting VARs, model selection, and shrinkage," Working Papers 15-07, University of Mannheim, Department of Economics.
    13. Gefang, Deborah, 2014. "Bayesian doubly adaptive elastic-net Lasso for VAR shrinkage," International Journal of Forecasting, Elsevier, vol. 30(1), pages 1-11.
    14. Embaye, Weldensie T. & Zereyesus, Yacob A., 2017. "Measuring the value of housing services in household surveys: an application of machine learning approach," 2017 Annual Meeting, February 4-7, 2017, Mobile, Alabama 252851, Southern Agricultural Economics Association.
    15. Chang, Jinyuan & Guo, Bin & Yao, Qiwei, 2015. "High dimensional stochastic regression with latent factors, endogeneity and nonlinearity," Journal of Econometrics, Elsevier, vol. 189(2), pages 297-312.

    More about this item

    Keywords

    Time Series; Vector Auto Regression; Regularization; Lasso; Group Lasso; Oracle estimator;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • 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
    • E30 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - General (includes Measurement and Data)
    • E40 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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