EFFICIENT ESTIMATION OF CONDITIONAL VARIANCE FUNCTIONS IN STOCHASTIC REGRESSION

Conditional heteroscedasticity has often been used in modelling and un derstanding the variability of statistical data. Under a general set-u p which includes nonlinear time: series models as a special case, we p ropose an efficient and adaptive method for estimating the conditional variance. The basic idea is to apply a local linear regression to the squared residuals. We demonstrate that, without knowing the regressio n function, we can estimate the conditional variance asymptotically as well as if the regression were given. This asymptotic result, establi shed under the assumption that the observations are made from a strict ly stationary and absolutely regular process, is also verified via sim ulation. Further, the asymptotic result paves the way for adapting an automatic bandwidth selection scheme. An application with financial da ta illustrates the usefulness of the proposed techniques.