Empirical Likelihood Inference for Functional Coefficient ARCH-M Model |
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Authors: | Hai Qing Zhao Yuan Li Yan Meng Zhao |
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Institution: | 1. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, P. R. China;2. School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang 524048, P. R. China;3. School of Economics and Statistics, Guangzhou University, Guangzhou 510006, P. R. China;4. School of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, P. R. China |
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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. |
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Keywords: | ARCH-M model empirical likelihood relative risk aversion |
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