ANOVA for diffusions and Itô processes

Details ANOVA for diffusions and Itô processes ANOVA for diffusions and Itô processes

2006-11-09

arxiv.org/abs/math/0611274v1

Annals of Statistics 2006, Vol. 34, No. 4, 1931-1963

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000000452 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000000452

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.

Affiliated with

Also associated with

No associations

Rating

ANOVA for diffusions and Itô processes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with ANOVA for diffusions and Itô processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and ANOVA for diffusions and Itô processes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-407859