## The Annals of Statistics

### ANOVA for diffusions and Itô processes

#### Abstract

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.

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.

#### Article information

Source
Ann. Statist., Volume 34, Number 4 (2006), 1931-1963.

Dates
First available in Project Euclid: 3 November 2006

https://projecteuclid.org/euclid.aos/1162567638

Digital Object Identifier
doi:10.1214/009053606000000452

Mathematical Reviews number (MathSciNet)
MR2283722

Zentralblatt MATH identifier
1246.91110

#### Citation

Mykland, Per Aslak; Zhang, Lan. ANOVA for diffusions and Itô processes. Ann. Statist. 34 (2006), no. 4, 1931--1963. doi:10.1214/009053606000000452. https://projecteuclid.org/euclid.aos/1162567638

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