We show that the empirical process of the squared residuals of an ARCH(p) sequence converges in distribution 1,0 a Gaussirm process B(F(t)) +t f(t) e, where F is the distribution function of the squared innovations, f its derivative, {B(tl, 0 <; t>1} a Brownian bridge and e a normal random variable.

We show that the empirical process of the squared residuals of an ARCH(p) sequence converges in distribution 1,0 a Gaussirm process B(F(t)) +t f(t) e, where F is the distribution function of the squared innovations, f its derivative, {B(tl, 0 <; t>1} a Brownian bridge and e a normal random variable.

This paper proposes efficient estimators of risk measures in a semiparametric GARCH model defined through moment constraints. Moment constraints are often used to identify and estimate the mean and variance parameters and are however discarded when estimating error quantiles. In order to prevent...