Asymptotic Expansion of the Risk Difference of the Bayesian Spectral   Density in the ARMA model
  The autoregressive moving average (ARMA) model is one of the most important models in time series analysis.We consider the Bayesian estimation of an unknown spectral density in the ARMA model.In the i.i.d. cases, Komaki showed that Bayesian predictive densities based on a superharmonic prior asymptotically dominate those based on the Jeffreys prior.It is shown by using the asymptotic expansion of the risk difference.We obtain the corresponding result in the ARMA model. 
Fuyuhiko Tanaka and Fumiyasu Komaki