Single-index volatility models and estimation

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-n 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. Copyright © 2002 Institute of Statistical Science, Academia Sinica.