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Shrinkage Estimation of Regression Models with Multiple Structural Changes

Author

Listed:
  • Junhui Qian

    (Antai College of Economics and Management, Shanghai Jiao Tong University)

  • Liangjun Su

    (Singapore Management University, School of Economics)

Abstract

In this paper we consider the problem of determining the number of structural changes in multiple linear regression models via group fused Lasso (least absolute shrinkage and selection operator ). We show that with probability tending to one our method can correctly determine the unknown number of breaks and the estimated break dates are sufficiently close to the true break dates. We obtain estimates of the regression coefficients via post Lasso and establish the asymptotic distributions of the estimates of both break ratios and regression coefficients. We also propose and validate a datadriven method to determine the tuning parameter. Monte Carlo simulations demonstrate that the proposed method works well in finite samples. We illustrate the use of our method with a predictive regression of the equity premium on fundamental information.

Suggested Citation

  • Junhui Qian & Liangjun Su, 2014. "Shrinkage Estimation of Regression Models with Multiple Structural Changes," Working Papers 06-2014, Singapore Management University, School of Economics.
    • Handle: RePEc:siu:wpaper:06-2014
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    Cited by:

    1. Ma, Shujie & Su, Liangjun, 2018. "Estimation of large dimensional factor models with an unknown number of breaks," Journal of Econometrics, Elsevier, vol. 207(1), pages 1-29.
    2. Yoshiyuki Kurachi & Kazuhiro Hiraki & Shinichi Nishioka, 2016. "Does a Higher Frequency of Micro-level Price Changes Matter for Macro Price Stickiness?: Assessing the Impact of Temporary Price Changes," Bank of Japan Working Paper Series 16-E-9, Bank of Japan.
    3. Guanyu Su & Junhui Qian, 2021. "Structural Changes in the Renminbi Exchange Rate Mechanism," China & World Economy, Institute of World Economics and Politics, Chinese Academy of Social Sciences, vol. 29(2), pages 1-23, March.
    4. Karsten Schweikert, 2022. "Detecting Multiple Structural Breaks in Systems of Linear Regression Equations with Integrated and Stationary Regressors," Papers 2201.05430, arXiv.org, revised Aug 2023.
    5. Wang, Wuyi & Su, Liangjun, 2021. "Identifying latent group structures in nonlinear panels," Journal of Econometrics, Elsevier, vol. 220(2), pages 272-295.
    6. Miao, Ke & Phillips, Peter C.B. & Su, Liangjun, 2023. "High-dimensional VARs with common factors," Journal of Econometrics, Elsevier, vol. 233(1), pages 155-183.
    7. Lee Jaeeun & Chen Jie, 2019. "A penalized regression approach for DNA copy number study using the sequencing data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 18(4), pages 1-14, August.
    8. Xu Cheng & Zhipeng Liao & Frank Schorfheide, 2016. "Shrinkage Estimation of High-Dimensional Factor Models with Structural Instabilities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(4), pages 1511-1543.
    9. Okui, Ryo & Wang, Wendun, 2021. "Heterogeneous structural breaks in panel data models," Journal of Econometrics, Elsevier, vol. 220(2), pages 447-473.
    10. Christis Katsouris, 2023. "High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods," Papers 2308.16192, arXiv.org.
    11. Gabriela Ciuperca, 2018. "Test by adaptive LASSO quantile method for real-time detection of a change-point," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(6), pages 689-720, August.
    12. Karsten Schweikert, 2020. "Oracle Efficient Estimation of Structural Breaks in Cointegrating Regressions," Papers 2001.07949, arXiv.org, revised Apr 2021.
    13. Karsten Schweikert, 2022. "Oracle Efficient Estimation of Structural Breaks in Cointegrating Regressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(1), pages 83-104, January.
    14. Tae-Hwy Lee & Shahnaz Parsaeian & Aman Ullah, 2022. "Efficient Combined Estimation under Structural Breaks," Advances in Econometrics, in: Essays in Honor of M. Hashem Pesaran: Prediction and Macro Modeling, volume 43, pages 119-142, Emerald Group Publishing Limited.
    15. Behrendt, Simon & Schweikert, Karsten, 2021. "A Note on Adaptive Group Lasso for Structural Break Time Series," Econometrics and Statistics, Elsevier, vol. 17(C), pages 156-172.
    16. Weijie Cui & Yong Li, 2023. "Bicluster Analysis of Heterogeneous Panel Data via M-Estimation," Mathematics, MDPI, vol. 11(10), pages 1-19, May.
    17. Gabriela Ciuperca & Matúš Maciak, 2020. "Change‐point detection in a linear model by adaptive fused quantile method," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 425-463, June.
    18. Berndt Jesenko & Christian Schlögl, 2021. "The effect of web of science subject categories on clustering: the case of data-driven methods in business and economic sciences," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(8), pages 6785-6801, August.
    19. Skrobotov Anton, 2023. "Testing for explosive bubbles: a review," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-26, January.
    20. Qian, Junhui & Su, Liangjun, 2014. "Structural change estimation in time series regressions with endogenous variables," Economics Letters, Elsevier, vol. 125(3), pages 415-421.
    21. Ma, Chenchen & Tu, Yundong, 2023. "Shrinkage estimation of multiple threshold factor models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1876-1892.
    22. Qian, Junhui & Su, Liangjun, 2016. "Shrinkage estimation of common breaks in panel data models via adaptive group fused Lasso," Journal of Econometrics, Elsevier, vol. 191(1), pages 86-109.
    23. Ma, Chenchen & Tu, Yundong, 2023. "Group fused Lasso for large factor models with multiple structural breaks," Journal of Econometrics, Elsevier, vol. 233(1), pages 132-154.

    More about this item

    Keywords

    Change point; Fused Lasso; Group Lasso; Penalized least squares; Structural change;
    All these keywords.

    JEL classification:

    • 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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