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Chi-Square-Type Distributions For Heavy-Tailed Variates

Author

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  • Mittnik, Stefan
  • Rachev, Svetlozar T.
  • Kim, Jeong-Ryeol

Abstract

The distribution of sums of squared random variables with heavy-tailed distributions is investigated. Considering random variables in the domain of attraction of a stable Paretian law we derive the limiting distribution as the degrees of freedom approach infinity. The finite-degrees-of-freedom behavior for stable Paretian variates is simulated. Response surface techniques are employed to compactly summarize the simulation results for a relevant range of significance levels.

Suggested Citation

  • Mittnik, Stefan & Rachev, Svetlozar T. & Kim, Jeong-Ryeol, 1998. "Chi-Square-Type Distributions For Heavy-Tailed Variates," Econometric Theory, Cambridge University Press, vol. 14(3), pages 339-354, June.
    • Handle: RePEc:cup:etheor:v:14:y:1998:i:03:p:339-354_14
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    Cited by:

    1. Hill, Jonathan B. & Aguilar, Mike, 2013. "Moment condition tests for heavy tailed time series," Journal of Econometrics, Elsevier, vol. 172(2), pages 255-274.
    2. Kurz-Kim, Jeong-Ryeol & Loretan, Mico, 2014. "On the properties of the coefficient of determination in regression models with infinite variance variables," Journal of Econometrics, Elsevier, vol. 181(1), pages 15-24.
    3. Hansen, Gerd, 2000. "The German labour market and the unification shock," Economic Modelling, Elsevier, vol. 17(3), pages 439-454, August.
    4. Hansen, Gerd & Kim, Jeong-Ryeol & Mittnik, Stefan, 1998. "Testing cointegrating coefficients in vector autoregressive error correction models," Economics Letters, Elsevier, vol. 58(1), pages 1-5, January.

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