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On modeling heterogeneity in linear models using trend polynomials

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  • Michaelides, Michael
  • Spanos, Aris

Abstract

The primary aim of the paper is to consider the problems and issues raised when the data exhibit time heterogeneity in the context of linear models. Ignoring time heterogeneity will undermine the reliability of inference and will give rise to untrustworthy evidence. Accounting for it using trend polynomials, however, is non-trivial because it raises several modeling issues. First, when the degree of the polynomial is greater than 4, or so, one needs to deal with the near-multicollinearity problem that arises. The second issue pertains to the type of polynomial that will adequately account for the time heterogeneity. Third, when the trend polynomials are treated as additional regressors, they will give rise to highly misleading statistical results. The paper investigates how different types of polynomials could deal with the near-multicollinearity and the modeling issues they raise, and makes recommendations to practitioners.

Suggested Citation

  • Michaelides, Michael & Spanos, Aris, 2020. "On modeling heterogeneity in linear models using trend polynomials," Economic Modelling, Elsevier, vol. 85(C), pages 74-86.
    • Handle: RePEc:eee:ecmode:v:85:y:2020:i:c:p:74-86
    DOI: 10.1016/j.econmod.2019.05.008
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    References listed on IDEAS

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    1. Spanos, Aris, 2010. "Akaike-type criteria and the reliability of inference: Model selection versus statistical model specification," Journal of Econometrics, Elsevier, vol. 158(2), pages 204-220, October.
    2. Choi,In, 2015. "Almost All about Unit Roots," Cambridge Books, Cambridge University Press, number 9781107482500.
    3. Phillips, Peter C.B., 2005. "Challenges of trending time series econometrics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(5), pages 401-416.
    4. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    5. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    6. Friend, Irwin & Blume, Marshall E, 1970. "Measurement of Portfolio Performance Under Uncertainty," American Economic Review, American Economic Association, vol. 60(4), pages 561-575, September.
    7. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    8. Moore, Henry Ludwell, 1914. "Economics Cycles: Their law and cause," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number moore1914.
    9. Spanos,Aris, 2019. "Probability Theory and Statistical Inference," Cambridge Books, Cambridge University Press, number 9781316636374.
    10. Fama, Eugene F. & French, Kenneth R., 2015. "A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
    11. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    12. Blume, Marshall E, 1970. "Portfolio Theory: A Step Toward Its Practical Application," The Journal of Business, University of Chicago Press, vol. 43(2), pages 152-173, April.
    13. Spanos, Aris & McGuirk, Anya, 2002. "The problem of near-multicollinearity revisited: erratic vs systematic volatility," Journal of Econometrics, Elsevier, vol. 108(2), pages 365-393, June.
    14. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    15. Inyoung Kim & Noah D. Cohen & Raymond J. Carroll, 2003. "Semiparametric Regression Splines in Matched Case-Control Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 1158-1169, December.
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    Cited by:

    1. Michael Michaelides & Niraj Poudyal, 2024. "Good risk measures, bad statistical assumptions, ugly risk forecasts," The Financial Review, Eastern Finance Association, vol. 59(2), pages 519-543, May.

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    More about this item

    Keywords

    Linear model; t-Heterogeneity; Near-collinearity; Trend polynomial; Orthogonal polynomial; Orthonormal polynomial;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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