  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 $L_2$-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.
