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Boosting nonlinear additive autoregressive time series

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  • Shafik, Nivien
  • Tutz, Gerhard

Abstract

Several methods for the analysis of nonlinear time series models have been proposed. As in linear autoregressive models the main problems are model identification, estimation and prediction. A boosting method is proposed that performs model identification and estimation simultaneously within the framework of nonlinear autoregressive time series. The method allows one to select influential terms from a large number of potential lags and exogenous variables. The influence of the selected terms is modeled by an expansion in basis function allowing for a flexible additive form of the predictor. The approach is very competitive in particular in high dimensional settings where alternative fitting methods fail. This is demonstrated by means of simulations and two applications to real world data.

Suggested Citation

  • Shafik, Nivien & Tutz, Gerhard, 2009. "Boosting nonlinear additive autoregressive time series," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2453-2464, May.
  • Handle: RePEc:eee:csdana:v:53:y:2009:i:7:p:2453-2464
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    References listed on IDEAS

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    1. Gatu, Cristian & Kontoghiorghes, Erricos J. & Gilli, Manfred & Winker, Peter, 2008. "An efficient branch-and-bound strategy for subset vector autoregressive model selection," Journal of Economic Dynamics and Control, Elsevier, vol. 32(6), pages 1949-1963, June.
    2. Hofmann, Marc & Gatu, Cristian & Kontoghiorghes, Erricos John, 2007. "Efficient algorithms for computing the best subset regression models for large-scale problems," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 16-29, September.
    3. De Gooijer, Jan G. & Ray, Bonnie K., 2003. "Modeling vector nonlinear time series using POLYMARS," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 73-90, February.
    4. Jianhua Z. Huang & Lijian Yang, 2004. "Identification of non-linear additive autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 463-477.
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    Cited by:

    1. Klaus Wohlrabe & Teresa Buchen, 2014. "Assessing the Macroeconomic Forecasting Performance of Boosting: Evidence for the United States, the Euro Area and Germany," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(4), pages 231-242, July.
    2. Christmann, Andreas & Hable, Robert, 2012. "Consistency of support vector machines using additive kernels for additive models," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 854-873.
    3. Souhaib Ben Taieb & Rob J Hyndman, 2014. "Boosting multi-step autoregressive forecasts," Monash Econometrics and Business Statistics Working Papers 13/14, Monash University, Department of Econometrics and Business Statistics.
    4. repec:eee:csdana:v:112:y:2017:i:c:p:88-98 is not listed on IDEAS
    5. Marra, Giampiero & Wood, Simon N., 2011. "Practical variable selection for generalized additive models," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2372-2387, July.
    6. Buchen, Teresa & Wohlrabe, Klaus, 2011. "Forecasting with many predictors: Is boosting a viable alternative?," Economics Letters, Elsevier, vol. 113(1), pages 16-18, October.
    7. Nikolay Robinzonov & Gerhard Tutz & Torsten Hothorn, 2012. "Boosting techniques for nonlinear time series models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(1), pages 99-122, January.

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