The problem of testing for the parametric form of the conditional variance is considered
in a fully nonparametric regression model. A test statistic based on a weighted
L2-distance between the empirical characteristic functions of residuals constructed
under the null hypothesis and under the alternative is proposed and studied theoretically.
The null asymptotic distribution of the test statistic is obtained and employed
to approximate the critical values. Finite sample properties of the proposed test are
numerically investigated in several Monte Carlo experiments. The developed results
assume independent data. Their extension to dependent observations is also discussed.