Abstract: This paper gives the asymptotic theory of a class of
Cramér-von Mises statistics for the m-sample
problem pertaining to the empirical processes based on the square residuals from
a class of ARCH models. An important aspect is that, unlike the residuals of
ARMA models the asymptotic distribution depends on those of ARCH volatility
estimators. Based on the asymptotics of we numerically assess the relative
asymptotic efficiency and ARCH volatility effect for some ARCH residual
distributions. Then this aspect of based on such residual
distributions is illustrated numerically. In contrast with the independent,
identically distributed or ARMA settings, these studies illuminate some
interesting features of ARCH residuals.
