  The problem of detecting variance breaks in the case of smooth time-varying
variance structure is studied. It is highlighted that the tests based on
(piecewise) constant specification of the variance are not able to distinguish
between smooth non constant variance and the case where an abrupt change is
present. Consequently, a new procedure for detecting variance breaks taking
into account for smooth changes of the variance is proposed. The finite sample
properties of the tests introduced in the paper are investigated by Monte Carlo
experiments. The theoretical outputs are illustrated using U.S. macroeconomic
data.
