Wavelet Linear Density Estimation for a GARCH Model under Various Dependence Structures
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Abstract:
We consider n observations from the GARCH-type model: S = σ2Z, where σ2 and Z are independent random variables. We develop a new wavelet linear estimator of the unknown density of σ2 under four different dependence structures: the strong mixing case, the β- mixing case, the pairwise positive quadrant case and the ρ-mixing case. Its asymptotic mean integrated squared error properties are explored. In each case, we prove that it attains a fast rate of convergence.
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Journal title
volume 11 issue None
pages 1- 21
publication date 2012-03
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