Premium
Kernel deconvolution of stochastic volatility models
Author(s) -
Comte Fabienne
Publication year - 2004
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2004.01825.x
Subject(s) - mathematics , deconvolution , stochastic volatility , nonparametric statistics , estimator , autoregressive model , kernel (algebra) , statistics , volatility (finance) , white noise , kernel smoother , econometrics , kernel method , combinatorics , computer science , artificial intelligence , radial basis function kernel , support vector machine
. In this paper, we study the problem of the nonparametric estimation of the function m in a stochastic volatility model h t = exp( X t /2λ) ξ t , X t = m ( X t −1 ) + η t , where ξ t is a Gaussian white noise. We show that the model can be written as an autoregression with errors‐in‐variables. Then an adaptation of the deconvolution kernel estimator proposed by Fan and Truong [ Annals of Statistics , 21, (1993) 1900] estimates the function m with the optimal rate, which depends on the distribution of the measurement error. The rates vary from powers of n to powers of ln( n ) depending on the rate of decay near infinity of the characteristic function of this noise. The performance of the method are studied by some simulation experiments and some real data are also examined.