Asymptotic Results for the Fourier Estimator of the Integrated Quarticity

31 Pages Posted: 5 Dec 2018 Last revised: 26 Jun 2019

See all articles by Giulia Livieri

Giulia Livieri

Scuola Normale Superiore

Maria Elvira Mancino

University of Florence - Department of Economics and Management

Stefano Marmi

Scuola Normale Superiore

Date Written: November 4, 2018

Abstract

In this paper we prove a central limit theorem for the Fourier quarticity estimator proposed in Mancino and Sanfelici (2012). In particular, we obtain a new consistency result and we show that the estimator reaches the parametric rate ρ(n)1/2, where ρ(n), is the discretization mesh and n the number of points of such a discretization. The optimal variance is obtained, with a suitable choice of the number of frequencies employed to compute the Fourier coefficients of the volatility, while the limiting distribution has a bias. As a by-product, thanks to the Fourier methodology, we obtain consistent estimators of any even power of the volatility function as well as an estimator of the spot quarticity. We assess the finite sample performance of the Fourier quarticity estimator in a numerical simulation by extending the analysis in Mancino and Sanfelici (2012). with different market microstructure frictions.

Keywords: (powers of) volatility estimation, quarticity, central limit theorem, Fourier analysis, high frequency data

JEL Classification: C13, C14, C58, G10

Suggested Citation

Livieri, Giulia and Mancino, Maria Elvira and Marmi, Stefano, Asymptotic Results for the Fourier Estimator of the Integrated Quarticity (November 4, 2018). Available at SSRN: https://ssrn.com/abstract=3278113

Giulia Livieri (Contact Author)

Scuola Normale Superiore ( email )

Piazza dei Cavalieri, 7
Pisa, 56126
Italy

Maria Elvira Mancino

University of Florence - Department of Economics and Management ( email )

Via delle Pandette, 32
Florence, Firenze 50127
Italy

HOME PAGE: http://www.unifi.it

Stefano Marmi

Scuola Normale Superiore ( email )

Piazza dei Cavalieri, 7
Pisa, 56126
Italy
+39050509064 (Phone)
+39050563513 (Fax)

HOME PAGE: http://homepage.sns.it/marmi/

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