@article {IOPORT.05697492,
    author       = {Tanaka, Fuyuhiko and Komaki, Fumiyasu},
    title        = {A superharmonic prior for the autoregressive process of the second-order.},
    year         = {2008},
    journal      = {Journal of Time Series Analysis},
    volume       = {29},
    number       = {3},
    issn         = {0143-9782},
    pages        = {444-452},
    publisher    = {Wiley-Blackwell, Oxford},
    doi          = {10.1111/j.1467-9892.2007.00561.x},
    abstract     = {The authors deal with a Bayesian approach to estimation of the spectral density of an $AR(p)$ process based on the Kullback-Leibler divergence. A superharmonic prior on the model is proposed as a non-informative prior rather than the Jeffreys prior. Theoretically, the Bayesian spectral density estimator based on it dominates asymptotically the one based on the Jeffreys prior under the Kullback-Leibler divergence. {\it F. Komaki} [Ann. Stat. 34, No. 2, 808--819 (2006; Zbl 1092.62037)] pointed out that a sufficient condition for the existence of superharmonic priors is that the model manifold of a parametric statistical model endowed with the Fisher metric has a non-positive sectional curvature. {\it F. Tanaka} and {\it F. Komaki} [Tensor, New Ser. 64, No. 2, 131--143 (2003; Zbl 1165.62339)] evaluated the sign of the sectional curvature of the AR model manifold with the above motivation. They showed that the sectional curvature on the AR(2) model always has a negative sign, while those on the $AR(p)$ models $(p>3)$ could have a positive sign at some points. Thus, it was shown that there exists a superharmonic prior (at least) for the AR(2) process. In the present article, an explicit form of the superharmonic prior for the AR(2) process is presented and compared with the Jeffreys prior in computer simulations.},
    reviewer     = {Mikhail P. Moklyachuk (Ky\"\i v)},
    identifier   = {05697492},
}