Oracle Efficient Estimation and Forecasting with the Adaptive LASSO and the Adaptive Group LASSO in Vector Autoregressions
AbstractWe show that the adaptive Lasso (aLasso) and the adaptive group Lasso (agLasso) are oracle efficient in stationary vector autoregressions where the number of parameters per equation is smaller than the number of observations. In particular, this means that the parameters are estimated consistently at root T rate, that the truly zero parameters are classiffied as such asymptotically and that the non-zero parameters are estimated as efficiently as if only the relevant variables had been included in the model from the outset. The group adaptive Lasso differs from the adaptive Lasso by dividing the covariates into groups whose members are all relevant or all irrelevant. Both estimators have the property that they perform variable selection and estimation in one step. We evaluate the forecasting accuracy of these estimators for a large set of macroeconomic variables. The Lasso is found to be the most precise procedure overall. The adaptive and the adaptive group Lasso are less stable but mostly perform at par with the common factor models.
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Bibliographic InfoPaper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2012-38.
Date of creation: 09 Jan 2012
Date of revision:
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Web page: http://www.econ.au.dk/afn/
Vector autoregression; VAR; adaptive Lasso; Group Lasso; Forecasting; Factor models; LSTAR.;
Find related papers by JEL classification:
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
- E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
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- Anders Bredahl Kock & Laurent A.F. Callot, 2012. "Oracle Inequalities for High Dimensional Vector Autoregressions," CREATES Research Papers 2012-16, School of Economics and Management, University of Aarhus.
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- Wang, Hansheng & Leng, Chenlei, 2008. "A note on adaptive group lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5277-5286, August.
- Hansheng Wang & Guodong Li & Chih-Ling Tsai, 2007. "Regression coefficient and autoregressive order shrinkage and selection via the lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 63-78.
- Leeb, Hannes & P tscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(01), pages 21-59, February.
- Anders Bredahl Kock & Timo Teräsvirta, 2011. "Forecasting Macroeconomic Variables using Neural Network Models and Three Automated Model Selection Techniques," CREATES Research Papers 2011-27, School of Economics and Management, University of Aarhus.
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