Itô processes are the most common form of continuous semimartingales, and include diffusion processes. This paper is concerned with the nonparametric regression relationship between two such Itô processes. We are interested in the quadratic variation (integrated volatility) of the residual in this regression, over a unit of time (such as a day). A main conceptual finding is that this quadratic variation can be estimated almost as if the residual process were observed, the difference being that there is also a bias which is of the same asymptotic order as the mixed normal error term.
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The proposed methodology, “ANOVA for diffusions and Itô processes,” can be used to measure the statistical quality of a parametric model and, nonparametrically, the appropriateness of a one-regressor model in general. On the other hand, it also helps quantify and characterize the trading (hedging) error in the case of financial applications.
Publié le : 2006-08-14
Classification:
ANOVA,
continuous semimartingale,
statistical uncertainty,
goodness of fit,
discrete sampling,
parametric and nonparametric estimation,
small interval asymptotics,
stable convergence,
option hedging,
60G44,
62M09,
62M10,
91B28,
60G42,
62G20,
62P20,
91B84
@article{1162567638,
author = {Mykland, Per Aslak and Zhang, Lan},
title = {ANOVA for diffusions and It\^o processes},
journal = {Ann. Statist.},
volume = {34},
number = {1},
year = {2006},
pages = { 1931-1963},
language = {en},
url = {http://dml.mathdoc.fr/item/1162567638}
}
Mykland, Per Aslak; Zhang, Lan. ANOVA for diffusions and Itô processes. Ann. Statist., Tome 34 (2006) no. 1, pp. 1931-1963. http://gdmltest.u-ga.fr/item/1162567638/