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Following this quote from a 4* econometrics journal,

"Note that a linear conditional mean model with ARCH disturbances can be described by a nonlinear specification without ARCH, i.e. the bilinear model. In this paper, we assume that the conditional mean is linear and is correctly specifed in the simulations to follow."

See the full paper here.

However, I seem to have some conflicting information here,

http://economia.unipv.it/pagp/pagine_personali/erossi-old/note32004a.pdf

Who say,

In contrast with the ARCH model in which the conditional variance is time varying, in the bilinear model the conditional variance is constant.

In regards to a bilinear model, if the conditional variance is constant how can this characterize ARCH effects.

A bonus answer would show how I could simulate a bilinear GARCH model.

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