  We analyse the prequential plug-in codes relative to one-parameter
exponential families M. We show that if data are sampled i.i.d. from some
distribution outside M, then the redundancy of any plug-in prequential code
grows at rate larger than 1/2 ln(n) in the worst case. This means that plug-in
codes, such as the Rissanen-Dawid ML code, may behave inferior to other
important universal codes such as the 2-part MDL, Shtarkov and Bayes codes, for
which the redundancy is always 1/2 ln(n) + O(1). However, we also show that a
slight modification of the ML plug-in code, "almost" in the model, does achieve
the optimal redundancy even if the the true distribution is outside M.
