Ljung and Caines[1,2 and 4], establish almost sure convergence and asymptotic normality of prediction error estimators for approximately identifying a given dynamical system as an element within a postulated class of models which need not necessarily include the sytem. These theorems amy be regarded as instances of a strong law of large numbers and a central limit theorem. This note complements the results of Ljung and Caines by establishing a Donsker functional central limit theorem, classical law of the iterated logarithm and Strassen functional law of the iterated logarithm for prediction error estimators These results may be used to find almost sure rates of convergence as well as limiting distributions of various functionals of the sequence of estimators