Asymptotic Expansion of the Risk Difference of the Bayesian Spectral Density in the ARMA model

Details Asymptotic Expansion of the Risk Difference of the Bayesian Spectral Density in the ARMA model Asymptotic Expansion of the Risk Difference of the Bayesian Spectral Density in the ARMA model

2005-10-26

arxiv.org/abs/math/0510558v1

Mathematics

Statistics Theory

23 pages

Scientific paper

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.

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