Asymptotic results for the Fourier estimator of the integrated quarticity

Giulia Livieri (), Maria Elvira Mancino and Stefano Marmi ()
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Giulia Livieri: Scuola Normale Superiore
Stefano Marmi: Scuola Normale Superiore

Decisions in Economics and Finance, 2019, vol. 42, issue 2, No 7, 502 pages

Abstract: Abstract In this paper, we prove a central limit theorem for an estimator of the integrated quarticity based on Fourier analysis, strictly related to the one proposed in Mancino and Sanfelici (Quant Finance 12: 607–622, 2012). Also, a consistency result is derived. We show that the estimator reaches the parametric rate $$\rho (n)^{1/2}$$ρ(n)1/2, where $$\rho (n)$$ρ(n) is the discretization mesh and n the number of points of such 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.

Keywords: (Powers of) volatility estimation; Quarticity; Central limit theorem; Fourier analysis; High-frequency data. (search for similar items in EconPapers)
JEL-codes: C13 C14 C58 G10 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10203-019-00259-6

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