Efficient nonparametric estimation and inference for the volatility function

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 $GARCH(1,1)$ model in terms of a Nonparametric-ARCH$\left(1\right)$ 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.

KEYWORDS:

• Nonparametric volatility estimation
• optimal bandwidth estimation
• confidence intervals
• testing for symmetry

MSC CODES:

• 62G08
• 65D10
• 91G70
• 82C32

Acknowledgements

We thank an anonymous referee for useful suggestions, which have significantly contributed to improving the quality of the publication.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Maria Lucia Parrella http://orcid.org/0000-0001-9151-2922

Additional information

Funding

Financial support by the Italian Ministry of Education, University and Research (MIUR), PRIN Research Project 2010–2011 – prot. 2010J3LZEN, ‘Forecasting economic and financial time series: understanding the complexity and modelling structural change’, is gratefully acknowledged.