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Acta Mathematica Sinica, English Series

, Volume 35, Issue 2, pp 270–296 | Cite as

Empirical Likelihood Inference for Functional Coefficient ARCH-M Model

  • Hai Qing Zhao
  • Yuan LiEmail author
  • Yan Meng Zhao
Article
  • 14 Downloads

Abstract

Empirical likelihood inference for parametric and nonparametric parts in functional coefficient ARCH-M models is investigated in this paper. Firstly, the kernel smoothing technique is used to estimate coefficient function δ(x). In this way we obtain an estimated function with parameter β. Secondly, the empirical likelihood method is developed to estimate the parameter β. An estimated empirical log-likelohood ratio is proved to be asymptotically standard chi-squred, and the maximum empirical likelihood estimation (MELE) for β is shown to be asymptotically normal. Finally, based on the MELE of β, the empirical likelihood approach is again applied to reestimate the nonparametric part δ(x). The empirical log-likelohood ratio for δ(x) is proved to be also asymptotically standard chi-squred. Simulation study shows that the proposed method works better than the normal approximation method in terms of average areas of confidence regions for β, and the empirical likelihood confidence belt for δ(x) performs well.

Keywords

ARCH-M model empirical likelihood relative risk aversion 

MR(2010) Subject Classification

62G05 62G20 

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science (CAS), Chinese Mathematical Society (CAS) and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and Information ScienceGuangzhou UniversityGuangzhouP. R. China
  2. 2.School of Mathematics and StatisticsLingnan Normal UniversityZhanjiangP. R. China
  3. 3.School of Economics and StatisticsGuangzhou UniversityGuangzhouP. R. China
  4. 4.School of Mathematics and StatisticsShenzhen UniversityShenzhenP. R. China

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