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Asymptotic expansion of the risk difference of the Bayesian spectral density in the autoregressive moving average model

Abstract

The autoregressive moving average (ARMA) model is one of the most important models in time series analysis. We consider Bayesian estimation of an unknown spectral density in the ARMA model. In i.i.d. cases, it is known that Bayesian predictive densities based on a superharmonic prior asymptotically dominate those based on the Jeffreys prior. It was shown by using the asymptotic expansion of the risk difference. We obtain the corresponding results for the ARMA model.

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Correspondence to Fuyuhiko Tanaka.

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Tanaka, F., Komaki, F. Asymptotic expansion of the risk difference of the Bayesian spectral density in the autoregressive moving average model. Sankhya A 73, 162–184 (2011). https://doi.org/10.1007/s13171-011-0005-1

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  • DOI: https://doi.org/10.1007/s13171-011-0005-1

AMS (2000) subject classification

  • Primary 62M15
  • Secondary 53B21

Keywords and phrases

  • Autoregressive moving average model
  • Bayesian estimation
  • information geometry
  • noninformative prior
  • spectral density