Year: 2022
Author: Cong Wu, Jinru Wang, Xiaochen Zeng
Journal of Computational Mathematics, Vol. 40 (2022), Iss. 1 : pp. 108–126
Abstract
This paper considers adaptive point-wise estimations of density functions in GARCH-type model under the local Hölder condition by wavelet methods. A point-wise lower bound estimation of that model is first investigated; then we provide a linear wavelet estimate to obtain the optimal convergence rate, which means that the convergence rate coincides with the lower bound. The non-linear wavelet estimator is introduced for adaptivity, although it is nearly-optimal. However, the non-linear wavelet one depends on an upper bound of the smoothness index of unknown functions, we finally discuss a data driven version without any assumptions on the estimated functions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2007-m2020-0109
Journal of Computational Mathematics, Vol. 40 (2022), Iss. 1 : pp. 108–126
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Wavelets Point-wise risk Thresholding Data-driven GARCH-type model.