Statistica Sinica 12(2002), 785-799

SINGLE-INDEX VOLATILITY MODELS AND ESTIMATION

Yingcun Xia$^{1,2}$, Howell Tong$^{3,4}$ and W. K. Li$^3$

$^1$University of Cambridge, $^2$Jinan University,

$^3$University of Hong Kong and $^4$London School of Economics

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-$n$ 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.

Key words and phrases: ARCH, conditional variance, local linear smoother, order determination.