We examine a method recently proposed by Hinich and Patterson (mimeo, Unive
rsity of Texas at Austin, 1995) for testing the validity of specifying a GA
RCH error structure for financial time series data in the context of a set
of ten daily Sterling exchange rates. The results demonstrate that there ar
e statistical structures present in the data that cannot be captured by a G
ARCH model, or any of its variants. This result has important implications
for the interpretation of the recent voluminous literature which attempts t
o model financial asset returns using this family of models.