ANOVA for diffusions and It\^{o} processes
Abstract
It\^{o} 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 It\^{o} 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. The proposed methodology, ``ANOVA for diffusions and It\^{o} 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.
Cite
@article{arxiv.math/0611274,
title = {ANOVA for diffusions and It\^{o} processes},
author = {Per Aslak Mykland and Lan Zhang},
journal= {arXiv preprint arXiv:math/0611274},
year = {2008}
}
Comments
Published at http://dx.doi.org/10.1214/009053606000000452 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)