We deal with bootstrapping tests for detecting conditional heteroskedasticity in the context of standard and nonstandard ARCH models. We develope parametric and nonparametric bootstrap tests based both on the LM statistic and a neural statistic. The neural tests are designed to approximate an arbitrary nonlinear form of the conditional variance by a neural function. While published tests are valid asymptotically, they are not exact in finite samples and suffer from a substantial size distortion: the finite-sample error remains non-negligible, even for several hundred observations. Here, we treat this problem using bootstrap methods, making possible a better finite-sample estimate of the distribution of the test statistic. A graphical presentation employing a size-correction principle is used to show the true power of the tests rather than the spurious nominal power typically given