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Estimating confidence regions over bounded domains

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  • Eklund, Bruno

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

Abstract

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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Bibliographic Info

Paper provided by Stockholm School of Economics in its series 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

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Keywords: Kernel estimation; nonlinear grid; GARCH model; highest density region;

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References

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  1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  2. Teräsvirta, Timo, 1996. "Two Stylized Facts and the Garch (1,1) Model," Working Paper Series in Economics and Finance 96, 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. He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 92(1), pages 173-192, September.
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Cited by:
  1. Lorenzo Pascual & Esther Ruiz & Diego Fresoli, 2011. "Bootstrap forecast of multivariate VAR models without using the backward representation," Statistics and Econometrics Working Papers ws113426, Universidad Carlos III, Departamento de Estadística y Econometría.
  2. Malmsten, Hans & Teräsvirta, Timo, 2004. "Stylized Facts of Financial Time Series and Three Popular Models of Volatility," Working Paper Series in Economics and Finance 563, Stockholm School of Economics, revised 03 Sep 2004.
  3. Ane, Thierry, 2006. "An analysis of the flexibility of Asymmetric Power GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1293-1311, November.

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