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Estimating High-Dimensional Time Series Models


  • Marcelo C. Medeiros

    () (Pontifical Catholic University of Rio de Janeiro)

  • Eduardo F. Mendes

    () (Pontifical Catholic University of Rio de Janeiro)


We study the asymptotic properties of the Adaptive LASSO (adaLASSO) in sparse, high-dimensional, linear time-series models. We assume both the number of covariates in the model and candidate variables can increase with the number of observations and the number of candidate variables is, possibly, larger than the number of observations. We show the adaLASSO consistently chooses the relevant variables as the number of observations increases (model selection consistency), and has the oracle property, even when the errors are non-Gaussian and conditionally heteroskedastic. A simulation study shows the method performs well in very general settings. Finally, we consider two applications: in the first one the goal is to forecast quarterly US inflation one-step ahead, and in the second we are interested in the excess return of the S&P 500 index. The method used outperforms the usual benchmarks in the literature.

Suggested Citation

  • Marcelo C. Medeiros & Eduardo F. Mendes, 2012. "Estimating High-Dimensional Time Series Models," CREATES Research Papers 2012-37, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2012-37

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    References listed on IDEAS

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    Cited by:

    1. Camila Epprecht & Dominique Guegan & Álvaro Veiga & Joel Correa da Rosa, 2017. "Variable selection and forecasting via automated methods for linear models: LASSO/adaLASSO and Autometrics," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00917797, HAL.
    2. Audrino, Francesco & Camponovo, Lorenzo & Roth, Constantin, 2015. "Testing the lag structure of assets’ realized volatility dynamics," Economics Working Paper Series 1501, University of St. Gallen, School of Economics and Political Science.
    3. Monbet, Valérie & Ailliot, Pierre, 2017. "Sparse vector Markov switching autoregressive models. Application to multivariate time series of temperature," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 40-51.
    4. Matteo Barigozzi & Christian T. Brownlees, 2013. "Nets: Network estimation for time series," Economics Working Papers 1391, Department of Economics and Business, Universitat Pompeu Fabra.
    5. Florian Ziel, 2015. "Iteratively reweighted adaptive lasso for conditional heteroscedastic time series with applications to AR-ARCH type processes," Papers 1502.06557,, revised Dec 2015.
    6. 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.
    7. Audrino, Francesco & Camponovo, Lorenzo, 2013. "Oracle Properties and Finite Sample Inference of the Adaptive Lasso for Time Series Regression Models," Economics Working Paper Series 1327, University of St. Gallen, School of Economics and Political Science.
    8. Matteo Barigozzi & Marc Hallin, 2015. "Networks, Dynamic Factors, and the Volatility Analysis of High-Dimensional Financial Series," Papers 1510.05118,, revised Jul 2016.
    9. Baek, Changryong & Davis, Richard A. & Pipiras, Vladas, 2017. "Sparse seasonal and periodic vector autoregressive modeling," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 103-126.
    10. Kascha, Christian & Trenkler, Carsten, 2015. "Forecasting VARs, model selection, and shrinkage," Working Papers 15-07, University of Mannheim, Department of Economics.
    11. Camila Epprecht & Dominique Guegan & Álvaro Veiga, 2013. "Comparing variable selection techniques for linear regression: LASSO and Autometrics," Documents de travail du Centre d'Economie de la Sorbonne 13080, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    12. Ziel, Florian, 2016. "Iteratively reweighted adaptive lasso for conditional heteroscedastic time series with applications to AR–ARCH type processes," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 773-793.

    More about this item


    sparse models; shrinkage; LASSO; adaLASSO; time series; forecasting.;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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