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

Author

Listed:
  • Alessandro Casini

    () (Boston University)

  • Pierre Perron

    () (Boston University)

Abstract

Building upon the continuous record asymptotic framework recently introduced by Casini and Perron (2017a) 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. The procedure relies on a Laplace-type estimator defined by an integration-based rather than an optimization-based method. A transformation of the least-integration-based 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 defined as 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 proposed is shown to have lower MAE and RMSE, and the confidence sets strike the best 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, 2017. "Continuous Record Laplace-based Inference about the Break Date in Structural Change Models," Boston University - Department of Economics - Working Papers Series WP2018-011, Boston University - Department of Economics.
  • Handle: RePEc:bos:wpaper:wp2018-011
    as

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    File URL: http://people.bu.edu/perron/papers/CASINI_PERRON_Lap_CR_single_Inf.pdf
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    References listed on IDEAS

    as
    1. Elliott, Graham & Muller, Ulrich K., 2007. "Confidence sets for the date of a single break in linear time series regressions," Journal of Econometrics, Elsevier, vol. 141(2), pages 1196-1218, December.
    2. repec:eee:econom:v:200:y:2017:i:1:p:36-47 is not listed on IDEAS
    3. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    4. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    5. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261, September.
    6. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
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    Cited by:

    1. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    2. Yaein Baek, 2018. "Estimation of Structural Break Point in Linear Regression Models," Papers 1811.03720, arXiv.org, revised May 2019.

    More about this item

    Keywords

    Asymptotic distribution; bias; break date; change-point; Generalized Laplace; infill asymptotics; semimartingale;

    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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