- This paper presents a series based test for regression functional forms. Compared with the tests of Hong and White [Hong, Y.M., and White, H., 1995. Consistent Specification Testing via Nonparametric Series Regression, Econometrica, 63, 1133-1159.], our test imposes weaker conditions on the approximating base functions, avoids non-zero center terms and allows for optimal smoothing. 2006 Elsevier B.V. All rights reserved.