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August 2006 ANOVA for diffusions and Itô processes
Per Aslak Mykland, Lan Zhang
Ann. Statist. 34(4): 1931-1963 (August 2006). DOI: 10.1214/009053606000000452

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.

Citation

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Per Aslak Mykland. Lan Zhang. "ANOVA for diffusions and Itô processes." Ann. Statist. 34 (4) 1931 - 1963, August 2006. https://doi.org/10.1214/009053606000000452

Information

Published: August 2006
First available in Project Euclid: 3 November 2006

zbMATH: 1246.91110
MathSciNet: MR2283722
Digital Object Identifier: 10.1214/009053606000000452

Subjects:
Primary: 60G44 , 62M09 , 62M10 , 91B28
Secondary: 60G42 , 62G20 , 62P20 , 91B84

Keywords: ANOVA , continuous semimartingale , discrete sampling , goodness of fit , option hedging , parametric and nonparametric estimation , small interval asymptotics , stable convergence , statistical uncertainty

Rights: Copyright © 2006 Institute of Mathematical Statistics

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Vol.34 • No. 4 • August 2006
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