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Minimax estimation for time series models

Author

Listed:
  • Yan Liu

    (Waseda University)

  • Masanobu Taniguchi

    (Waseda University)

Abstract

The minimax principle is very important for all the fields of statistical science. The minimax approach is to choose an estimator which protects against the largest risk possible. In this paper we show that the Whittle estimator becomes a minimax estimator for the prediction error loss. It is shown that the Whittle estimator is a Bayes estimator for Jeffreys’ prior. Because the minimax approach is very immature in time series analysis, the result shows another advantage of the Whittle estimator.

Suggested Citation

  • Yan Liu & Masanobu Taniguchi, 2021. "Minimax estimation for time series models," METRON, Springer;Sapienza Università di Roma, vol. 79(3), pages 353-359, December.
    • Handle: RePEc:spr:metron:v:79:y:2021:i:3:d:10.1007_s40300-021-00217-6
    DOI: 10.1007/s40300-021-00217-6
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    References listed on IDEAS

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    1. Taniguchi, M. & Krishnaiah, P. R., 1987. "Asymptotic distributions of functions of the eigenvalues of sample covariance matrix and canonical correlation matrix in multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 22(1), pages 156-176, June.
    2. 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.
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    Cited by:

    1. Xiaofei Xu & Yan Liu & Masanobu Taniguchi, 2023. "Higher‐order asymptotics of minimax estimators for time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(2), pages 247-257, March.

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