A Class of Nonlinear ARCH Models.

A class of nonlinear autoregressive conditional heteroskedasticity models is suggested. The proposed class encompasses several functional forms for autoregressive conditional heteroskedasticity which have been put forth in the literature. A Lagrange multiplier test is developed to test Engle's autoregressive conditional heteroskedasticity specification against the wider class of models. This test provides an easily computed disgnostic check of the adequacy of an autoregressive conditional heteroskedasticity model after it has been estimated. The theory is applied to a number of weekly exchange rate series and the authors find strong evidence of nonlinear autoregressive conditional heteroskedasticity. Copyright 1992 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.