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Estimating confidence regions over bounded domains

  • Eklund, Bruno


    (Dept. of Economic Statistics, Stockholm School of Economics)

Estimating a density function over a bounded domain can be very complicated and resulting in an unsatisfactory or unrealistic density estimate. In many cases a one-to-one transformation can be applied to the considered data set, but there are also situations where such a unique transformation may not exist. This paper proposes a method to estimate confidence regions over bounded domains when a one-to-one transformation either does not exist or its existence is difficult to verify. By taking into account parameter restrictions of a underlying model, a nonlinear grid can be constructed, over which the density function can be estimated. The method is illustrated by applying it to the kurtosis/first-order autocorrelation of squared observations of the GARCH(1,1) model.

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Paper provided by Stockholm School of Economics in its series SSE/EFI Working Paper Series in Economics and Finance with number 548.

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Length: 12 pages
Date of creation: 28 Nov 2003
Date of revision:
Publication status: Published in Computational Statistics and Data Analysis, 2005, pages 349-360.
Handle: RePEc:hhs:hastef:0548
Contact details of provider: Postal: The Economic Research Institute, Stockholm School of Economics, P.O. Box 6501, 113 83 Stockholm, Sweden
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  1. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  2. He, Changli & Teräsvirta, Timo, 1997. "Properties of Moments of a Family of GARCH Processes," SSE/EFI Working Paper Series in Economics and Finance 198, Stockholm School of Economics.
  3. Tim Ramsay, 2002. "Spline smoothing over difficult regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 307-319.
  4. Teräsvirta, Timo, 1996. "Two Stylized Facts and the Garch (1,1) Model," SSE/EFI Working Paper Series in Economics and Finance 96, Stockholm School of Economics.
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