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Large Vector Auto Regressions

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  • Song Song
  • Peter J. Bickel
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    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 \textit{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 \textit{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.

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    File URL: http://arxiv.org/pdf/1106.3915
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1106.3915.

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    Date of creation: Jun 2011
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    Handle: RePEc:arx:papers:1106.3915

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    Web page: http://arxiv.org/

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    1. Martha Banbura & Domenico Giannone & Lucrezia Reichlin, 2008. "Large Bayesian VARs," Working Papers ECARES 2008_033, ULB -- Universite Libre de Bruxelles.
    2. Francis X. Diebold & Canlin Li, 2004. "Forecasting the Term Structure of Government Bond Yields," CFS Working Paper Series 2004/09, Center for Financial Studies.
    3. Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1986. "Forecasting and conditional projection using realistic prior distribution," Staff Report 93, Federal Reserve Bank of Minneapolis.
    4. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 1998. "Monetary Policy Shocks: What Have We Learned and to What End?," NBER Working Papers 6400, National Bureau of Economic Research, Inc.
    5. Fengler, Matthias R. & Härdle, Wolfgang & Mammen, Enno, 2003. "Implied volatility string dynamics," SFB 373 Discussion Papers 2003,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. Alexander Chudik & M. Hashem Pesaran, 2009. "Infinite-dimensional VARs and factor models," Working Paper Series 998, European Central Bank.
    7. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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    Cited by:
    1. 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.

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