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Model Selection in Equations with Many 'Small' Effects

Author

Listed:
  • Jennifer L. Castle

    (Magdalen College and Institute for New Economic Thinking, Oxford Martin School, University of Oxford, UK)

  • Jurgen A. Doornik

    (Economics Department and Institute for New Economic Thinking, Oxford Martin School, University of Oxford, UK)

  • David F. Hendry

    (Economics Department and Institute for New Economic Thinking, Oxford Martin School, University of Oxford, UK)

Abstract

High dimensional general unrestricted models (GUMs) may include important individual determinants, many small relevant effects, and irrelevant variables. Automatic model selection procedures can handle more candidate variables than observations, allowing substantial dimension reduction from GUMs with salient regressors, lags, non-linear transformations, and multiple location shifts, together with all the principal components, possibly representing 'factor' structures, as perfect collinearity is also unproblematic. 'Factors' can capture small influences that selection may not retain individually. The final model can implicitly include more variables than observations, entering via 'factors'. We simulate selection in several special cases to illustrate.

Suggested Citation

  • Jennifer L. Castle & Jurgen A. Doornik & David F. Hendry, 2012. "Model Selection in Equations with Many 'Small' Effects," Working Paper series 53_12, Rimini Centre for Economic Analysis.
    • Handle: RePEc:rim:rimwps:53_12
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    References listed on IDEAS

    as
    1. Jennifer Castle & David Hendry, 2010. "Automatic Selection for Non-linear Models," Economics Series Working Papers 473, University of Oxford, Department of Economics.
    2. Castle, Jennifer L. & Doornik, Jurgen A. & Hendry, David F., 2012. "Model selection when there are multiple breaks," Journal of Econometrics, Elsevier, vol. 169(2), pages 239-246.
    3. Anindya Banerjee & Massimiliano Marcellino & Igor Masten, 2008. "Forecasting Macroeconomic Variables Using Diffusion Indexes in Short Samples with Structural Change," Working Papers 334, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    4. David F. Hendry & Hans-Martin Krolzig, 2005. "The Properties of Automatic "GETS" Modelling," Economic Journal, Royal Economic Society, vol. 115(502), pages 32-61, March.
    5. Castle, Jennifer L. & Hendry, David F., 2010. "A low-dimension portmanteau test for non-linearity," Journal of Econometrics, Elsevier, vol. 158(2), pages 231-245, October.
    6. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    7. Carlos Santos & David Hendry & Soren Johansen, 2008. "Automatic selection of indicators in a fully saturated regression," Computational Statistics, Springer, vol. 23(2), pages 317-335, April.
    8. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    9. Jennifer Castle & David Hendry, 2012. "Forecasting by factors, by variables, or both?," Economics Series Working Papers 600, University of Oxford, Department of Economics.
    10. Massimiliano Marcellino & Carlo A. Favero & Francesca Neglia, 2005. "Principal components at work: the empirical analysis of monetary policy with large data sets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(5), pages 603-620.
    11. Leeb, Hannes & Pötscher, Benedikt M., 2003. "The Finite-Sample Distribution Of Post-Model-Selection Estimators And Uniform Versus Nonuniform Approximations," Econometric Theory, Cambridge University Press, vol. 19(1), pages 100-142, February.
    12. Espasa, Antoni & Mayo-Burgos, Iván, 2013. "Forecasting aggregates and disaggregates with common features," International Journal of Forecasting, Elsevier, vol. 29(4), pages 718-732.
    13. Hendry David F & Mizon Grayham E, 2011. "Econometric Modelling of Time Series with Outlying Observations," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-26, February.
    14. Jurgen A. Doornik, 2008. "Encompassing and Automatic Model Selection," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 915-925, December.
    15. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    16. Castle Jennifer L. & Doornik Jurgen A & Hendry David F., 2011. "Evaluating Automatic Model Selection," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-33, February.
    17. Søren Johansen & Bent Nielsen, 2008. "An analysis of the indicator saturation estimator as a robust regression," Discussion Papers 08-03, University of Copenhagen. Department of Economics.
    18. David F. Hendry, 2009. "The Methodology of Empirical Econometric Modeling: Applied Econometrics Through the Looking-Glass," Palgrave Macmillan Books, in: Terence C. Mills & Kerry Patterson (ed.), Palgrave Handbook of Econometrics, chapter 1, pages 3-67, Palgrave Macmillan.
    19. Castle, Jennifer L. & Hendry, David F., 2014. "Model selection in under-specified equations facing breaks," Journal of Econometrics, Elsevier, vol. 178(P2), pages 286-293.
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    Cited by:

    1. Rahul Verma & Rajesh Mohnot, 2023. "Relative Impact of the U.S. Energy Market Sentiments on Stocks and ESG Index Returns: Evidence from GCC Countries," International Journal of Energy Economics and Policy, Econjournals, vol. 13(2), pages 290-300, March.
    2. Jennifer Castle & David Hendry, 2012. "Forecasting by factors, by variables, or both?," Economics Series Working Papers 600, University of Oxford, Department of Economics.
    3. David F. Hendry & Felix Pretis, 2013. "Anthropogenic influences on atmospheric CO2," Chapters, in: Roger Fouquet (ed.), Handbook on Energy and Climate Change, chapter 12, pages 287-326, Edward Elgar Publishing.
    4. Castle, Jennifer L. & Clements, Michael P. & Hendry, David F., 2013. "Forecasting by factors, by variables, by both or neither?," Journal of Econometrics, Elsevier, vol. 177(2), pages 305-319.
    5. Jurgen A. Doornik & David F. Hendry & Steve Cook, 2015. "Statistical model selection with “Big Data”," Cogent Economics & Finance, Taylor & Francis Journals, vol. 3(1), pages 1045216-104, December.
    6. Yuxuan Huang, 2016. "Forecasting the USD/CNY Exchange Rate under Different Policy Regimes," Working Papers 2016-001, The George Washington University, Department of Economics, H. O. Stekler Research Program on Forecasting.

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    More about this item

    Keywords

    Model selection; high dimensionality; principal components; Monte Carlo;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • 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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