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Continuous Record Laplace-based Inference about the Break Date in Structural Change Models

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  • Alessandro Casini

    (University of Rome Tor Vergata)

  • Pierre Perron

    (Boston University)

Abstract

Building upon the continuous record asymptotic framework recently introduced by Casini and Perron (2020a) for inference in structural change models, we propose a Laplace-based (Quasi-Bayes) procedure for the construction of the estimate and confidence set for the date of a structural change. It is defined by an integration rather than an optimization-based method. A transformation of the least-squares criterion function is evaluated in order to derive a proper distribution, referred to as the Quasi-posterior. For a given choice of a loss function, the Laplace-type estimator is the minimizer of the expected risk with the expectation taken under the Quasi-posterior. Besides providing an alternative estimate that is more precise—lower mean absolute error (MAE) and lower root-mean squared error (RMSE)—than the usual least-squares one, the Quasi-posterior distribution can be used to construct asymptotically valid inference using the concept of Highest Density Region. The resulting Laplace-based inferential procedure is shown to have lower MAE and RMSE, and the confidence sets strike a better balance between empirical coverage rates and average lengths of the confidence sets relative to traditional long-span methods, whether the break size is small or large.

Suggested Citation

  • Alessandro Casini & Pierre Perron, 2020. "Continuous Record Laplace-based Inference about the Break Date in Structural Change Models," Boston University - Department of Economics - Working Papers Series WP2020-014, Boston University - Department of Economics.
  • Handle: RePEc:bos:wpaper:wp2020-014
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    Cited by:

    1. 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.
    2. 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.
    3. Casini, Alessandro, 2023. "Theory of evolutionary spectra for heteroskedasticity and autocorrelation robust inference in possibly misspecified and nonstationary models," Journal of Econometrics, Elsevier, vol. 235(2), pages 372-392.
    4. Shimizu, Kenichi, 2023. "Asymptotic properties of Bayesian inference in linear regression with a structural break," Journal of Econometrics, Elsevier, vol. 235(1), pages 202-219.
    5. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    6. Casini, Alessandro & Perron, Pierre, 2024. "Prewhitened long-run variance estimation robust to nonstationarity," Journal of Econometrics, Elsevier, vol. 242(1).
    7. 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.
    8. Alessandro Casini & Pierre Perron, 2018. "Continuous Record Asymptotics for Change-Points Models," Papers 1803.10881, arXiv.org, revised Nov 2021.
    9. Federico Belotti & Alessandro Casini & Leopoldo Catania & Stefano Grassi & Pierre Perron, 2023. "Simultaneous bandwidths determination for DK-HAC estimators and long-run variance estimation in nonparametric settings," Econometric Reviews, Taylor & Francis Journals, vol. 42(3), pages 281-306, February.
    10. Yaein Baek, 2018. "Estimation of a Structural Break Point in Linear Regression Models," Papers 1811.03720, arXiv.org, revised Jun 2020.

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    More about this item

    Keywords

    Asymptotic distribution; bias; break date; change-point; Generalized Laplace; infill asymptotics; semimartingale;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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