A class of nonlinear ARCH models. (English) Zbl 0744.62152

Summary: A class of nonlinear ARCH models is suggested. The proposed class encompasses several functional forms of ARCH which have been put forth in the literature. A Lagrange multiplier test is developed to test R. F. Engle’s ARCH specification [Econometrica 50, 987-1007 (1982; Zbl 0491.62099)] against a wider class of models. This test provides an easily computed diagnostic check of the adequacy of an ARCH model after it has been estimated. The theory is applied to a number of weakly exchange rate series and we find strong evidence of nonlinear ARCH.


62P20 Applications of statistics to economics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)


Zbl 0491.62099
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