Limit theorems in the Fourier transform method for the estimation of multivariate volatility

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:121

Article

Clement, Emmanuelle¹  Gloter, Arnaud² 

[1] Univ Paris Est, Lab Anal & Math Appl, F-77454 Marne La Vallee 2, France

[2] Univ Evry Val dEssonne, Dept Math, F-91025 Evry, France

关键词: Non-parametric estimation;    Ito process;    Fourier transform;    Weak convergence;   

DOI  :  10.1016/j.spa.2010.11.016

来源: Elsevier

【 摘 要 】

In this paper, we prove some limit theorems for the Fourier estimator of multivariate volatility proposed by Malliavin and Mancino (2002, 2009) [14,15]. In a general framework of discrete time observations we establish the convergence of the estimator and some associated central limit theorems with explicit asymptotic variance. In particular, our results show that this estimator is consistent for synchronous data, but possibly biased for non-synchronous observations. Moreover, from our general central limit theorem, we deduce that the estimator can be efficient in the case of a synchronous regular sampling. In the non-synchronous sampling case, the expression of the asymptotic variance is in general less tractable. We study this case more precisely through the example of an alternate sampling. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free