We introduce the notion of continuously invertible volatility models that
relies on some Lyapunov condition and some regularity condition. We show that
it is almost equivalent to the ability of the volatilities forecasting using
the parametric inference approach based on the SRE given in [16]. Under very
weak assumptions, we prove the strong consistency and the asymptotic normality
of the parametric inference. Based on this parametric estimation, a natural
strongly consistent forecast of the volatility is given.

This paper is devoted to the off-line multiple change-point detection in a
semiparametric framework. The time series is supposed to belong to a large
class of models including AR($\infty$), ARCH($\infty$), TARCH($\infty$),...
models where the coefficients change at each instant of breaks. The different
unknown parameters (number of changes, change dates and parameters of
successive models) are estimated using a penalized contrast built on
conditional quasi-likelihood.