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On Modeling Heteroskedasticity: The Student's t and Elliptical Linear Regression Models

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  • Spanos, Aris

Abstract

This paper proposes a new approach to modeling heteroskedastidty which enables the modeler to utilize information conveyed by data plots in making informed decisions on the form and structure of heteroskedasticity. It extends the well-known normal/linear/homoskedastic models to a family of non-normal/linear/heteroskedastic models. The non-normality is kept within the bounds of the elliptically symmetric family of multivariate distributions (and in particular the Student's t distribution) that lead to several forms of heteroskedasticity, including quadratic and exponential functions of the conditioning variables. The choice of the latter family is motivated by the fact that it enables us to model some of the main sources of heteroskedasticity: “thicktails,” individual heterogeneity, and nonlinear dependence. A common feature of the proposed class of regression models is that the weak exogeneity assumption is inappropriate. The estimation of these models, without the weak exogeneity assumption, is discussed, and the results are illustrated by using cross-section data on charitable contributions.

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  • Spanos, Aris, 1994. "On Modeling Heteroskedasticity: The Student's t and Elliptical Linear Regression Models," Econometric Theory, Cambridge University Press, vol. 10(02), pages 286-315, June.
  • Handle: RePEc:cup:etheor:v:10:y:1994:i:02:p:286-315_00
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    Cited by:

    1. Michael Haliassos, 2002. "Stockholding: Recent Lessons from Theory and Computations," University of Cyprus Working Papers in Economics 0206, University of Cyprus Department of Economics.
    2. Panos Hatzipanayotou & Sajal Lahiri & Michael S. Michael, 2002. "Reforms of Environmental Policies in the Presence of Cross-border Pollution and two Stage Clean Up," University of Cyprus Working Papers in Economics 0203, University of Cyprus Department of Economics.
    3. Jiro Hodoshima, 2004. "On weak exogeneity of the student's t and elliptical linear regression models," Econometric Society 2004 Far Eastern Meetings 601, Econometric Society.
    4. Panos Pashardes & Soteroula Hajispyrou, 2002. "Consumer Demand and Welfare under Increasing Block Pricing," University of Cyprus Working Papers in Economics 0207, University of Cyprus Department of Economics.
    5. Shuangzhe Liu & Chris Heyde & Wing-Keung Wong, 2011. "Moment matrices in conditional heteroskedastic models under elliptical distributions with applications in AR-ARCH models," Statistical Papers, Springer, vol. 52(3), pages 621-632, August.
    6. Spanos, Aris, 1995. "On theory testing in econometrics : Modeling with nonexperimental data," Journal of Econometrics, Elsevier, vol. 67(1), pages 189-226, May.
    7. Blake, David & Cairns, Andrew J. G. & Dowd, Kevin, 2001. "Pensionmetrics: stochastic pension plan design and value-at-risk during the accumulation phase," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 187-215, October.
    8. Caporale, Guglielmo Maria & Pittis, Nikitas, 1996. "Modelling the sterling-deutschmark exchange rate: Non-linear dependence and thick tails," Economic Modelling, Elsevier, vol. 13(1), pages 1-14, January.
    9. Psaradakis, Zacharias & Sola, Martin, 1996. "On the power of tests for superexogeneity and structural invariance," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 151-175.
    10. J. James Reade & Ulrich Volz, 2011. "From the General to the Specific," Discussion Papers 11-18, Department of Economics, University of Birmingham.
    11. Maria S. Heracleous, 2007. "Sample Kurtosis, GARCH-t and the Degrees of Freedom Issue," Economics Working Papers ECO2007/60, European University Institute.
    12. Caporale, Guglielmo Maria & Hassapis, Christis & Pittis, Nikitas, 1998. "Conditional Leptokurtosis and Non-Linear Dependence in Exchange Rate Returns," Journal of Policy Modeling, Elsevier, vol. 20(5), pages 581-601, October.

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