Whittle estimation of ARCH models

For a class of parametric ARCH models, Whittle estimation based on squared observations is shown to be [square root of n]-consistent and asymptotically normal. Our conditions require the squares to have short memory autocorrelation, by comparison with the work of Zaffaroni (1999, “Gaussian Inference on Certain Long-Range Dependent Volatility Models,” Preprint), who established the same properties on the basis of an alternative class of models with martingale difference levels and long memory autocorrelated squares.