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Efficient nonparametric estimation and inference for the volatility function
Statistics ( IF 1.9 ) Pub Date : 2019-05-20 , DOI: 10.1080/02331888.2019.1615066
Francesco Giordano 1 , Maria Lucia Parrella 1
Affiliation  

ABSTRACT In this paper we focus on nonparametric analysis of the volatility function for mixing processes. Our approach is based on local polynomial smoothing and supplies several tools which can be used to test a specific parametric model: nonparametric function estimation, nonparametric confidence intervals, and nonparametric test for symmetry. At the same time, it faces the main drawbacks of the nonparametric procedures proposed so far in the literature that are the choice of the bandwidth parameter and the slow convergence rate. Another aim of this paper is to focus on the advantages of an alternative representation for the parametric model in terms of a Nonparametric-ARCH model, to be estimated by local polynomials. We prove the consistency of the proposed method and investigate its empirical performance on synthetic and real datasets.

中文翻译:

波动率函数的有效非参数估计和推理

摘要 在本文中,我们重点研究混合过程的波动率函数的非参数分析。我们的方法基于局部多项式平滑,并提供了几种可用于测试特定参数模型的工具:非参数函数估计、非参数置信区间和非参数对称性检验。同时,它面临着迄今为止文献中提出的非参数程序的主要缺点,即带宽参数的选择和收敛速度慢。本文的另一个目的是关注参数模型在非参数 ARCH 模型方面的替代表示的优点,由局部多项式估计。我们证明了所提出方法的一致性,并研究了其在合成和真实数据集上的经验表现。
更新日期:2019-05-20
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