  We analyze the Dawid-Rissanen prequential maximum likelihood codes relative
to one-parameter exponential family models M. If data are i.i.d. according to
an (essentially) arbitrary P, then the redundancy grows at rate c/2 ln n. We
show that c=v1/v2, where v1 is the variance of P, and v2 is the variance of the
distribution m* in M that is closest to P in KL divergence. This shows that
prequential codes behave quite differently from other important universal codes
such as the 2-part MDL, Shtarkov and Bayes codes, for which c=1. This behavior
is undesirable in an MDL model selection setting.
