In this talk, we propose two parametric alternatives to
the standard GARCH model. They allow the conditional variance to have a
smooth time-varying structure of either additive or multiplicative
type. The suggested parameterizations describe both nonlinearity and
structural change in the conditional and unconditional variances where
the transition between regimes over time is smooth. A modelling
strategy for these new time-varying parameter GARCH models is
developed. It relies on a sequence of Lagrange multiplier tests, and
the adequacy of the estimated models is investigated by a Lagrange
multiplier type misspecification tests. Finite-sample properties of
these procedures and tests are examined by simulation. An empirical
application to stock returns and another one to exchange rate returns
illustrate the functioning and properties of our modelling strategy in
practice. The results show that the long memory type behaviour of the
sample autocorrelation functions of the absolute returns may be induced
by changes in the unconditional variance. |