## ANOVA FOR DIFFUSIONS AND ITO PROCESSES

Venue: | SUBMITTED TO THE ANNALS OF STATISTICS |

Citations: | 25 - 11 self |

### BibTeX

@MISC{Mykland_anovafor,

author = {Per Aslak Mykland and Lan Zhang},

title = { ANOVA FOR DIFFUSIONS AND ITO PROCESSES},

year = {}

}

### OpenURL

### Abstract

Ito processes are the most common form of continuous semimartingales, and include diffusion processes. The paper is concerned with the nonparametric regression relationship between two such Ito 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 Ito 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.