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. |