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Estimation of multiple-regime regressions with least absolutes deviation

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  • Jushan, Bai

Abstract

This paper considers least absolute deviations estimation of a regression model with multiple change points occurring at unknown times. Some asymptotic results, including rates of convergence and asymptotic distributions, for the estimated change points and the estimated regression coefficient are derived. Results are obtained without assuming that each regime spans a positive fraction of the sample size. In addition, the number of change points is allowed to grow as the sample size increases. Estimation of the number of change points is also considered. A feasible computational algorithm is developed. An application is also given, along with some monte carlo simulations.

Suggested Citation

  • Jushan, Bai, 1995. "Estimation of multiple-regime regressions with least absolutes deviation," MPRA Paper 32916, University Library of Munich, Germany, revised Feb 1998.
  • Handle: RePEc:pra:mprapa:32916
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    File URL: https://mpra.ub.uni-muenchen.de/32916/1/MPRA_paper_32916.pdf
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    References listed on IDEAS

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    1. Michael J. Dueker, 1992. "The response of market interest rates to discount rate changes," Review, Federal Reserve Bank of St. Louis, issue Jul, pages 78-91.
    2. Gombay, Edit & Horváth, Lajos, 1994. "Limit theorems for change in linear regression," Journal of Multivariate Analysis, Elsevier, vol. 48(1), pages 43-69, January.
    3. Bai, Jushan, 1995. "Least Absolute Deviation Estimation of a Shift," Econometric Theory, Cambridge University Press, vol. 11(03), pages 403-436, June.
    4. Bhattacharya, P.K., 1987. "Maximum likelihood estimation of a change-point in the distribution of independent random variables: General multiparameter case," Journal of Multivariate Analysis, Elsevier, vol. 23(2), pages 183-208, December.
    5. V. Vance Roley & Simon M. Wheatley, 1990. "Temporal Variation in the Interest-Rate Response to Money Announcements," NBER Working Papers 3471, National Bureau of Economic Research, Inc.
    6. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.
    2. Oka, Tatsushi & Qu, Zhongjun, 2011. "Estimating structural changes in regression quantiles," Journal of Econometrics, Elsevier, vol. 162(2), pages 248-267, June.
    3. Venkata Jandhyala & Stergios Fotopoulos & Ian MacNeill & Pengyu Liu, 2013. "Inference for single and multiple change-points in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 423-446, July.
    4. Woody, Jonathan & Lund, Robert, 2014. "A linear regression model with persistent level shifts: An alternative to infill asymptotics," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 118-124.
    5. Fiteni, Inmaculada, 2004. "[tau]-estimators of regression models with structural change of unknown location," Journal of Econometrics, Elsevier, vol. 119(1), pages 19-44, March.
    6. Gabriela Ciuperca, 2014. "Model selection by LASSO methods in a change-point model," Statistical Papers, Springer, vol. 55(2), pages 349-374, May.
    7. repec:eee:intfin:v:50:y:2017:i:c:p:52-68 is not listed on IDEAS

    More about this item

    Keywords

    Multiple change points; multiple-regime regressions; least absolute deviation; asymptotic distribution;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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