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ANOVA for diffusions

Mykland, P.A. and Zhang, L.

Abstract:

The paper examines the relationship among Ito processes from the angle of quadratic variation. The proposed methodology, ``ANOVA for diffusions'', allows drawing inference for a time interval, rather than for single time points. One of its applications is in fitness of modeling a stochastic process, it also helps quantify and characterize the trading (hedging) error in the case of financial applications.

The reason why the ANOVA permits conclusions over a time interval is that the asymptotic errors of the residual quadratic variation converge as a process (in time). A main conceptual finding was the clear cut effect of the two sources behind the asymptotics. The variation component (mixed Gaussian) comes only from the discretization error (in time discrete sampling). On the other hand, the bias depends only on the choice of estimator of the quadratic variation. This two-sources principle carries over to other criteria of goodness of fit, for example, the coefficient of determination.

Keywords: ANOVA, statistical uncertainty, Goodness of Fit, discrete sampling, nonparametric estimation, small interval asymptotics, stable convergence, option hedging, volatility model.

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