Stochastic Volatility (SV) models are widely used in financial applications. To decide whether standard parametric restrictions are justified for a given data set, a statistical test is required. In this paper, we develop such a test of a linear hypothesis versus a general composite nonparametric alternative using the state space representation of the SV model as an errors-in-variables AR(1) model. The power of the test is analyzed. We provide a simulation study and apply the test to the HFDF96 data set. Our results confirm a linear AR(1) structure in log-volatility for the analyzed stock indices S&P500, Dow Jones Industrial Average and for the exchange rate DEM/USD.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am30-4-3,
author = {D. Feldmann and W. H\"ardle and C. Hafner and M. Hoffmann and O. Lepski and A. Tsybakov},
title = {Testing Linearity in an AR Errors-in-variables Model with Application to Stochastic Volatility},
journal = {Applicationes Mathematicae},
volume = {30},
year = {2003},
pages = {389-412},
zbl = {1051.62108},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am30-4-3}
}
D. Feldmann; W. Härdle; C. Hafner; M. Hoffmann; O. Lepski; A. Tsybakov. Testing Linearity in an AR Errors-in-variables Model with Application to Stochastic Volatility. Applicationes Mathematicae, Tome 30 (2003) pp. 389-412. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am30-4-3/