Asymptotics of Rissanen's predictive stochastic complexity: from parametric to nonparametric models

It is shown that for a wide class of stationary ARMA processes J. Rissanen's predictive stochastic complexity (1986) is asymptotically equal to the lower bound provided by the Rissanen-Shannon inequality almost surely. An analogous theorem is proved for a more easily computable version of the predictive stochastic complexity based on the recursive estimation of the ARMA parameters.<>