Goodness-of-fit tests for kernel regression with an application to option implied volatilities

This paper proposes a test of a restricted specification of regression, bas ed on comparing residual sum of squares from kernel regression. Our main ca se is where both the restricted specification. and the general model are no nparametric, with our test equivalently viewed as a test of dimension reduc tion. We discuss practical features of implementing the test, and variation s applicable to testing parametric models as the null hypothesis, or semipa rametric models that depend on a finite parameter vector as well as unknown functions. We apply our testing procedure to option prices; we reject a pa rametric version of the Black-Scholes formula but fail to reject a semipara metric version against a general nonparametric regression. (C) 2001 Elsevie r Science S.A. All rights reserved.