A FOURIER TRANSFORM METHOD FOR NONPARAMETRIC ESTIMATION OF MULTIVARIATE VOLATILITY

被引：76
|
作者：
Malliavin, Paul [1 ]
Mancino, Maria Elvira [2 ]
机构：
[1] Inst France, Acad Sci, F-75004 Paris, France
[2] Univ Florence, Dept Math Decis, Florence, Italy
来源：
ANNALS OF STATISTICS | 2009年 / 37卷 / 04期
关键词：
Continuous semi-martingale; instantaneous co-volatility; nonparametric estimation; Fourier transform; high frequency data; HIGH-FREQUENCY DATA; MARKET MICROSTRUCTURE NOISE; INTEGRATED VOLATILITY; DIFFUSION-COEFFICIENT; COVARIANCE ESTIMATION; MODELS; SAMPLE; VARIANCE; FEEDBACK; PRICES;
D O I：
10.1214/08-AOS633
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous serni-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.
引用
收藏
页码：1983 / 2010
页数：28
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