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Non-regular estimation theory for piecewise continuous spectral densities

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  • Taniguchi, Masanobu

Abstract

For a class of Gaussian stationary processes, the spectral density f[theta]([lambda]),[theta]=([tau]',[eta]')', is assumed to be a piecewise continuous function, where [tau] describes the discontinuity points, and the piecewise spectral forms are smoothly parameterized by [eta]. Although estimating the parameter [theta] is a very fundamental problem, there has been no systematic asymptotic estimation theory for this problem. This paper develops the systematic asymptotic estimation theory for piecewise continuous spectra based on the likelihood ratio for contiguous parameters. It is shown that the log-likelihood ratio is not locally asymptotic normal (LAN). Two estimators for [theta], i.e., the maximum likelihood estimator and the Bayes estimator , are introduced. Then the asymptotic distributions of and are derived and shown to be non-normal. Furthermore we observe that is asymptotically efficient, but is not so. Also various versions of step spectra are considered.

Suggested Citation

  • Taniguchi, Masanobu, 2008. "Non-regular estimation theory for piecewise continuous spectral densities," Stochastic Processes and their Applications, Elsevier, vol. 118(2), pages 153-170, February.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:2:p:153-170
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    References listed on IDEAS

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    1. Dean Corbae & Sam Ouliaris & Peter C. B. Phillips, 2002. "Band Spectral Regression with Trending Data," Econometrica, Econometric Society, vol. 70(3), pages 1067-1109, May.
    2. Geweke, John F. & Singleton, Kenneth J., 1981. "Latent variable models for time series : A frequency domain approach with an application to the permanent income hypothesis," Journal of Econometrics, Elsevier, vol. 17(3), pages 287-304, December.
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    Cited by:

    1. Yan Liu & Masanobu Taniguchi, 2021. "Minimax estimation for time series models," METRON, Springer;Sapienza Università di Roma, vol. 79(3), pages 353-359, December.
    2. Ngai Chan & Yury Kutoyants, 2012. "On parameter estimation of threshold autoregressive models," Statistical Inference for Stochastic Processes, Springer, vol. 15(1), pages 81-104, April.

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