A FOURIER TRANSFORM METHOD FOR NONPARAMETRIC ESTIMATION OF MULTIVARIATE VOLATILITY

被引：80

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

页码：1983 / 2010

页数：28

共 44 条

[21] Realized variance and market microstructure noise [J].