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August 2009 A Fourier transform method for nonparametric estimation of multivariate volatility
Paul Malliavin, Maria Elvira Mancino
Ann. Statist. 37(4): 1983-2010 (August 2009). DOI: 10.1214/08-AOS633


We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous semi-martingales, which is based on Fourier analysis. The co-volatility is reconstructed as a stochastic function of time by establishing a connection between the Fourier transform of the prices process and the Fourier transform of the co-volatility process. A nonparametric estimator is derived given a discrete unevenly spaced and asynchronously sampled observations of the asset price processes. The asymptotic properties of the random estimator are studied: namely, consistency in probability uniformly in time and convergence in law to a mixture of Gaussian distributions.


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Paul Malliavin. Maria Elvira Mancino. "A Fourier transform method for nonparametric estimation of multivariate volatility." Ann. Statist. 37 (4) 1983 - 2010, August 2009.


Published: August 2009
First available in Project Euclid: 18 June 2009

zbMATH: 1168.62030
MathSciNet: MR2533477
Digital Object Identifier: 10.1214/08-AOS633

Primary: 42A38 , 62F12 , 62G05
Secondary: 60H10 , 62P20

Keywords: Continuous semi-martingale , Fourier transform , High frequency data , instantaneous co-volatility , nonparametric estimation

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.37 • No. 4 • August 2009
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