If the model is non stationary, can it be applied to stationary data/series?
For example the KPSS test shows that the data is stationary but the BP test shows presence of heteroscedasticity.
If a stationary model need a condition of stationary data to be applied but not on non stationary data, can a non stationary model be applied to stationary data?
Taken that the issue is with the model of non stationary ARCH without intercept where it is use for non stationary data. As the model is derived by setting the intercept = 0,
so does it means that the same can be applied to the stationary model where we set the intercept = 0 to be applied to the stationary data?
[An ARCH model without intercept] Christian M. Hafner, Arie Preminger
"In the stationary case, a well-known feature of classical ARCH models is that the intercept is notoriously difficult to estimate, as it is often very close to zero, and numerical difficulties arise for the inference. This problem is more dramatic in more complex ARCH-type models, where alternative estimation strategies have been proposed such as the variance targeting idea of Engle and Mezrich (1996). In the non-stationary framework of Jensen and Rahbek (2004), a direct analog of this idea is not available, since the unconditional variance of the process does not exist."