Summary: Journal of Econometrics 105 (2001) 363­412
www.elsevier.com/locate/econbase
Goodness-of-ÿt 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
Abstract
This paper proposes a test of a restricted speciÿcation of regression, based on
comparing residual sum of squares from kernel regression. Our main case is where
both the restricted speciÿcation 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 ÿnite 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: Aït-Sahalia, Yacine - Program in Applied and Comptutational Mathematics & Department of Economics, Princeton University

Collections: Mathematics