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Higher‐order asymptotics of minimax estimators for time series

Author

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  • Xiaofei Xu
  • Yan Liu
  • Masanobu Taniguchi

Abstract

We consider the minimax estimation of time series in view of higher‐order asymptotic theory. Under the framework of Bayesian inference, we focus on the Bayes estimator and the Bayesian Whittle estimator for parameter estimation. It is shown that these estimators are minimax with respect to the Bayes risk of higher‐order bias appeared in their asymptotic expansion. The minimax problem in the boundary issue with parameter on the boundary of parameter space is also discussed. Our theoretical discovery is justified by simulation studies even when the sample size is small.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:44:y:2023:i:2:p:247-257
    DOI: 10.1111/jtsa.12661
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    References listed on IDEAS

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    1. Adam M Sykulski & Sofia C Olhede & Arthur P Guillaumin & Jonathan M Lilly & Jeffrey J Early, 2019. "The debiased Whittle likelihood," Biometrika, Biometrika Trust, vol. 106(2), pages 251-266.
    2. Phillips, P C B, 1991. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 333-364, Oct.-Dec..
    3. Yan Liu & Masanobu Taniguchi, 2021. "Minimax estimation for time series models," METRON, Springer;Sapienza Università di Roma, vol. 79(3), pages 353-359, December.
    4. Sims, Christopher A & Uhlig, Harald, 1991. "Understanding Unit Rooters: A Helicopter Tour," Econometrica, Econometric Society, vol. 59(6), pages 1591-1599, November.
    5. Robinson, Peter M. & Velasco, Carlos, 2000. "Whittle pseudo-maximum likelihood estimation for nonstationary time series," LSE Research Online Documents on Economics 2273, London School of Economics and Political Science, LSE Library.
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