Estimating confidence regions over bounded domains
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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|Date of creation:||28 Nov 2003|
|Date of revision:|
|Publication status:||Published in Computational Statistics and Data Analysis, 2005, pages 349-360.|
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Journal of Econometrics,
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"Properties of moments of a family of GARCH processes,"
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- 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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