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New distribution theory for the estimation of structural break point in mean

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  • Jiang, Liang
  • Wang, Xiaohu
  • Yu, Jun

Abstract

Based on the Girsanov theorem, this paper obtains the exact distribution of the maximum likelihood estimator of structural break point in a continuous time model. The exact distribution is asymmetric and tri-modal, indicating that the estimator is biased. These two properties are also found in the finite sample distribution of the least squares (LS) estimator of structural break point in the discrete time model, suggesting the classical long-span asymptotic theory is inadequate. The paper then builds a continuous time approximation to the discrete time model and develops an in-fill asymptotic theory for the LS estimator. The in-fill asymptotic distribution is asymmetric and tri-modal and delivers good approximations to the finite sample distribution. To reduce the bias in the estimation of both the continuous time and the discrete time models, a simulation-based method based on the indirect estimation (IE) approach is proposed. Monte Carlo studies show that IE achieves substantial bias reductions.

Suggested Citation

  • Jiang, Liang & Wang, Xiaohu & Yu, Jun, 2018. "New distribution theory for the estimation of structural break point in mean," Journal of Econometrics, Elsevier, vol. 205(1), pages 156-176.
    • Handle: RePEc:eee:econom:v:205:y:2018:i:1:p:156-176
    DOI: 10.1016/j.jeconom.2018.03.009
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    References listed on IDEAS

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    Cited by:

    1. TAYANAGI, Toshikazu & 田柳, 俊和 & KUROZUMI, Eiji & 黒住, 英司, 2023. "Change-point estimators with the weighted objective function when estimating breaks one at a time," Discussion Papers 2023-04, Graduate School of Economics, Hitotsubashi University.
    2. Wang, Xiaohu & Xiao, Weilin & Yu, Jun, 2023. "Modeling and forecasting realized volatility with the fractional Ornstein–Uhlenbeck process," Journal of Econometrics, Elsevier, vol. 232(2), pages 389-415.
    3. Yaein Baek, 2018. "Estimation of a Structural Break Point in Linear Regression Models," Papers 1811.03720, arXiv.org, revised Jun 2020.
    4. Bykhovskaya, Anna & Phillips, Peter C.B., 2020. "Point optimal testing with roots that are functionally local to unity," Journal of Econometrics, Elsevier, vol. 219(2), pages 231-259.
    5. Gregory Cox, 2022. "A Generalized Argmax Theorem with Applications," Papers 2209.08793, arXiv.org.
    6. Alessandro Casini & Pierre Perron, 2018. "Continuous Record Asymptotics for Change-Points Models," Papers 1803.10881, arXiv.org, revised Nov 2021.
    7. Casini, Alessandro & Perron, Pierre, 2021. "Continuous record Laplace-based inference about the break date in structural change models," Journal of Econometrics, Elsevier, vol. 224(1), pages 3-21.
    8. Harris, David & Kew, Hsein & Taylor, A.M. Robert, 2020. "Level shift estimation in the presence of non-stationary volatility with an application to the unit root testing problem," Journal of Econometrics, Elsevier, vol. 219(2), pages 354-388.
    9. Tayanagi, Toshikazu & 田柳, 俊和 & Kurozumi, Eiji & 黒住, 英司, 2022. "In-fill asymptotic distribution of the change point estimator when estimating breaks one at a time," Discussion Papers 2022-03, Graduate School of Economics, Hitotsubashi University.

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    More about this item

    Keywords

    Structural break; Bias reduction; Indirect estimation; Exact distribution; In-fill asymptotics;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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