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.

中文翻译：

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非参数回归中方差函数的模型规格检验

在完全非参数的回归模型中考虑了测试条件方差的参数形式的问题。提出并基于零假设和替代条件下构造的残差经验特征函数之间的加权\（L_2 \）-距离的检验统计量。获得检验统计量的零渐近分布，并将其用于逼近临界值。在几个蒙特卡洛实验中，对提出的测试的有限样本属性进行了数值研究。得出的结果采用独立数据。还讨论了它们对从属观察的扩展。