Abstract: We develop a single-index volatility model in this paper. A new method is proposed to estimate the single-index coefficient and the link function. Unlike most existing estimation methods for semiparametric models, root- consistency of the single-index coefficient can be achieved by our method without under-smoothing the unknown function. A Lagrange-multiplier type test is employed to determine the order of the model. Some simulations and applications to real data are included.
Key words and phrases: ARCH, conditional variance, local linear smoother, order determination.