Testing for breaks in variance structures with smooth changes

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.