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Journal of Econometrics 105 (2001) 363412 www.elsevier.com/locate/econbase

Summary: Journal of Econometrics 105 (2001) 363­412
Goodness-of-˙t tests for kernel regression with
an application to option implied volatilities
Yacine A t-Sahaliaa;
, Peter J. Bickelb
, Thomas M. Stokerc
aDepartment of Economics, Princeton University, Princeton, NJ 08544-1021, USA
bDepartment of Statistics, University of Calfornia, Berkeley, CA 94720-3860, USA
cSloan School of Management, MIT, Cambridge, MA 02142-1347, USA
Received 28 February 2000; revised 13 March 2001; accepted 30 April 2001
This paper proposes a test of a restricted speci˙cation of regression, based on
comparing residual sum of squares from kernel regression. Our main case is where
both the restricted speci˙cation and the general model are nonparametric, with our test
equivalently viewed as a test of dimension reduction. We discuss practical features of
implementing the test, and variations applicable to testing parametric models as the
null hypothesis, or semiparametric models that depend on a ˙nite parameter vector as
well as unknown functions. We apply our testing procedure to option prices; we reject
a parametric version of the Black­Scholes formula but fail to reject a semiparametric


Source: Aīt-Sahalia, Yacine - Program in Applied and Comptutational Mathematics & Department of Economics, Princeton University


Collections: Mathematics