[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v204y2018i1p66-85.html
   My bibliography  Save this article

Testing for common breaks in a multiple equations system

Author

Listed:
  • Oka, Tatsushi
  • Perron, Pierre
Abstract
The issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null hypothesis is that breaks in different parameters occur at common locations and are separated by some positive fraction of the sample size unless they occur across different equations. Under the alternative hypothesis, the break dates across parameters are not the same and also need not be separated by a positive fraction of the sample size whether within or across equations. The test considered is the quasi-likelihood ratio test assuming normal errors, though as usual the limit distribution of the test remains valid with non-normal errors. Of independent interest, we provide results about the rate of convergence of the estimates when searching over all possible partitions subject only to the requirement that each regime contains at least as many observations as some positive fraction of the sample size, allowing break dates not separated by a positive fraction of the sample size across equations. Simulations show that the test has good finite sample properties. We also provide an application to issues related to level shifts and persistence for various measures of inflation to illustrate its usefulness.

Suggested Citation

  • Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.
    • Handle: RePEc:eee:econom:v:204:y:2018:i:1:p:66-85
    DOI: 10.1016/j.jeconom.2018.01.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407618300071
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2018.01.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Kejriwal, Mohitosh & Perron, Pierre, 2010. "Testing for Multiple Structural Changes in Cointegrated Regression Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 503-522.
    2. Hall, Alastair R. & Han, Sanggohn & Boldea, Otilia, 2012. "Inference regarding multiple structural changes in linear models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 170(2), pages 281-302.
    3. Kim, Dukpa & Oka, Tatsushi & Estrada, Francisco & Perron, Pierre, 2020. "Inference related to common breaks in a multivariate system with joined segmented trends with applications to global and hemispheric temperatures," Journal of Econometrics, Elsevier, vol. 214(1), pages 130-152.
    4. Kurozumi, Eiji & Tuvaandorj, Purevdorj, 2011. "Model selection criteria in multivariate models with multiple structural changes," Journal of Econometrics, Elsevier, vol. 164(2), pages 218-238, October.
    5. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    6. Deng, Ai & Perron, Pierre, 2008. "A non-local perspective on the power properties of the CUSUM and CUSUM of squares tests for structural change," Journal of Econometrics, Elsevier, vol. 142(1), pages 212-240, January.
    7. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2007. "Testing for unit roots in time series models with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 140(2), pages 919-947, October.
    8. Jushan, Bai, 1995. "Estimation of multiple-regime regressions with least absolutes deviation," MPRA Paper 32916, University Library of Munich, Germany, revised Feb 1998.
    9. Breitung, Jörg & Eickmeier, Sandra, 2011. "Testing for structural breaks in dynamic factor models," Journal of Econometrics, Elsevier, vol. 163(1), pages 71-84, July.
    10. Jushan Bai, 1994. "Least Squares Estimation Of A Shift In Linear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(5), pages 453-472, September.
    11. Pierre Perron & Yohei Yamamoto, 2015. "Using OLS to Estimate and Test for Structural Changes in Models with Endogenous Regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(1), pages 119-144, January.
    12. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    13. Su, Liangjun & Xiao, Zhijie, 2008. "Testing for parameter stability in quantile regression models," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2768-2775, November.
    14. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(4), pages 489-500, December.
    15. Kim, Dukpa & Perron, Pierre, 2009. "Assessing the relative power of structural break tests using a framework based on the approximate Bahadur slope," Journal of Econometrics, Elsevier, vol. 149(1), pages 26-51, April.
    16. Todd E. Clark, 2006. "Disaggregate evidence on the persistence of consumer price inflation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(5), pages 563-587, July.
    17. Deng, Ai & Perron, Pierre, 2008. "The Limit Distribution Of The Cusum Of Squares Test Under General Mixing Conditions," Econometric Theory, Cambridge University Press, vol. 24(3), pages 809-822, June.
    18. Pierre Perron & Yohei Yamamoto, 2016. "On the Usefulness or Lack Thereof of Optimality Criteria for Structural Change Tests," Econometric Reviews, Taylor & Francis Journals, vol. 35(5), pages 782-844, May.
    19. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    20. Hall, Alastair R & Sen, Amit, 1999. "Structural Stability Testing in Models Estimated by Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(3), pages 335-348, July.
    21. Zhongjun Qu & Pierre Perron, 2007. "Estimating and Testing Structural Changes in Multivariate Regressions," Econometrica, Econometric Society, vol. 75(2), pages 459-502, March.
    22. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July.
    23. Yunjong Eo & James Morley, 2015. "Likelihood‐ratio‐based confidence sets for the timing of structural breaks," Quantitative Economics, Econometric Society, vol. 6(2), pages 463-497, July.
    24. Qu, Zhongjun, 2008. "Testing for structural change in regression quantiles," Journal of Econometrics, Elsevier, vol. 146(1), pages 170-184, September.
    25. Hansen, Bruce E, 2002. "Tests for Parameter Instability in Regressions with I(1) Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 45-59, January.
    26. 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.
    27. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    28. Kim, Dukpa, 2011. "Estimating a common deterministic time trend break in large panels with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 164(2), pages 310-330, October.
    29. Corradi, Valentina & Swanson, Norman R., 2014. "Testing for structural stability of factor augmented forecasting models," Journal of Econometrics, Elsevier, vol. 182(1), pages 100-118.
    30. Perron, Pierre & Yamamoto, Yohei, 2014. "A Note On Estimating And Testing For Multiple Structural Changes In Models With Endogenous Regressors Via 2sls," Econometric Theory, Cambridge University Press, vol. 30(2), pages 491-507, April.
    31. Bai, Jushan, 2010. "Common breaks in means and variances for panel data," Journal of Econometrics, Elsevier, vol. 157(1), pages 78-92, July.
    32. Han, Xu & Inoue, Atsushi, 2015. "Tests For Parameter Instability In Dynamic Factor Models," Econometric Theory, Cambridge University Press, vol. 31(5), pages 1117-1152, October.
    33. Kejriwal, Mohitosh & Perron, Pierre, 2008. "The limit distribution of the estimates in cointegrated regression models with multiple structural changes," Journal of Econometrics, Elsevier, vol. 146(1), pages 59-73, September.
    34. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
    35. Oka, Tatsushi & Qu, Zhongjun, 2011. "Estimating structural changes in regression quantiles," Journal of Econometrics, Elsevier, vol. 162(2), pages 248-267, June.
    36. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
    37. Corradi, Valentina, 1999. "Deciding Between I(0) And I(1) Via Flil-Based Bounds," Econometric Theory, Cambridge University Press, vol. 15(5), pages 643-663, October.
    38. Baltagi, Badi H. & Feng, Qu & Kao, Chihwa, 2016. "Estimation of heterogeneous panels with structural breaks," Journal of Econometrics, Elsevier, vol. 191(1), pages 176-195.
    39. 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.
    40. Bai, Jushan, 1995. "Least Absolute Deviation Estimation of a Shift," Econometric Theory, Cambridge University Press, vol. 11(3), pages 403-436, June.
    41. Yamamoto, Yohei & Tanaka, Shinya, 2015. "Testing for factor loading structural change under common breaks," Journal of Econometrics, Elsevier, vol. 189(1), pages 187-206.
    42. Jushan Bai, 2000. "Vector Autoregressive Models with Structural Changes in Regression Coefficients and in Variance-Covariance Matrices," Annals of Economics and Finance, Society for AEF, vol. 1(2), pages 303-339, November.
    43. Perron, Pierre, 1990. "Testing for a Unit Root in a Time Series with a Changing Mean," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 153-162, April.
    44. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(1), pages 1-21, March.
    45. Grayham E. Mizon & David F. Hendry, 1998. "Exogeneity, causality, and co-breaking in economic policy analysis of a small econometric model of money in the UK," Empirical Economics, Springer, vol. 23(3), pages 267-294.
    46. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    47. Jushan Bai & Robin L. Lumsdaine & James H. Stock, 1998. "Testing For and Dating Common Breaks in Multivariate Time Series," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 395-432.
    48. Dukpa Kim & Tatsushi Oka & Francisco Estrada & Pierre Perron, 2017. "Inference Related to Common Breaks in a Multivariate System with Joined Segmented Trends with Applications to Global and Hemispheric Temperatures," Boston University - Department of Economics - Working Papers Series WP2017-003, Boston University - Department of Economics.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Claudio Morana, 2014. "Factor Vector Autoregressive Estimation of Heteroskedastic Persistent and Non Persistent Processes Subject to Structural Breaks," Working Papers 273, University of Milano-Bicocca, Department of Economics, revised May 2014.
    2. Kim, Dukpa & Oka, Tatsushi & Estrada, Francisco & Perron, Pierre, 2020. "Inference related to common breaks in a multivariate system with joined segmented trends with applications to global and hemispheric temperatures," Journal of Econometrics, Elsevier, vol. 214(1), pages 130-152.
    3. 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.
    4. Manner, Hans & Blatt, Dominik & Candelon, Bertrand, 2014. "Detecting financial contagion in a multivariate system," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100411, Verein für Socialpolitik / German Economic Association.
    5. Perron, Pierre & Yamamoto, Yohei, 2014. "A Note On Estimating And Testing For Multiple Structural Changes In Models With Endogenous Regressors Via 2sls," Econometric Theory, Cambridge University Press, vol. 30(2), pages 491-507, April.
    6. Yunjong Eo & James Morley, 2015. "Likelihood‐ratio‐based confidence sets for the timing of structural breaks," Quantitative Economics, Econometric Society, vol. 6(2), pages 463-497, July.
    7. Smith, Simon C. & Timmermann, Allan & Zhu, Yinchu, 2019. "Variable selection in panel models with breaks," Journal of Econometrics, Elsevier, vol. 212(1), pages 323-344.
    8. Pierre L. Siklos, 2020. "Looking into the Rear-View Mirror: Lessons from Japan for the Eurozone and the U.S?," IMES Discussion Paper Series 20-E-02, Institute for Monetary and Economic Studies, Bank of Japan.
    9. Alexander Berglund & Massimo Guidolin & Manuela Pedio, 2020. "Monetary policy after the crisis: A threat to hedge funds' alphas?," Journal of Asset Management, Palgrave Macmillan, vol. 21(3), pages 219-238, May.
    10. Josep Lluís Carrion‐i‐Silvestre & María Dolores Gadea, 2023. "Testing for multiple level shifts with an integrated or stationary noise component," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(6), pages 801-819, September.
    11. Ye Li & Pierre Perron, 2017. "Inference on locally ordered breaks in multiple regressions," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 289-353, March.
    12. Mugrabi, Farah Daniela, 2023. "Detecting and dating possibly distinct structural breaks in the covariance structure of financial assets," LIDAM Discussion Papers LFIN 2023001, Université catholique de Louvain, Louvain Finance (LFIN).
    13. Ye Li & Pierre Perron, 2013. "Inference Related to Locally Ordered and Common Breaks in a Multivariate System with Joined Segmented Trends," Boston University - Department of Economics - Working Papers Series 2013-010, Boston University - Department of Economics.
    14. Karsten Schweikert, 2022. "Detecting Multiple Structural Breaks in Systems of Linear Regression Equations with Integrated and Stationary Regressors," Papers 2201.05430, arXiv.org, revised Sep 2024.
    15. Karsten Schweikert, 2020. "Oracle Efficient Estimation of Structural Breaks in Cointegrating Regressions," Papers 2001.07949, arXiv.org, revised Apr 2021.
    16. Bergamelli, Michele & Bianchi, Annamaria & Khalaf, Lynda & Urga, Giovanni, 2019. "Combining p-values to test for multiple structural breaks in cointegrated regressions," Journal of Econometrics, Elsevier, vol. 211(2), pages 461-482.
    17. Richard S. J. Tol & Francisco Estrada & Carlos Gay-García, 2012. "The persistence of shocks in GDP and the estimation of the potential economic costs of climate change," Working Paper Series 4312, Department of Economics, University of Sussex Business School.
    18. Jiang, Peiyun & Kurozumi, Eiji, 2021. "A new test for common breaks in heterogeneous panel data models," Discussion paper series HIAS-E-107, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    19. Blatt, Dominik & Candelon, Bertrand & Manner, Hans, 2015. "Detecting contagion in a multivariate time series system: An application to sovereign bond markets in Europe," Journal of Banking & Finance, Elsevier, vol. 59(C), pages 1-13.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Boston University - Department of Economics - Working Papers Series WP2019-02, Boston University - Department of Economics.
    2. Oka, Tatsushi & Qu, Zhongjun, 2011. "Estimating structural changes in regression quantiles," Journal of Econometrics, Elsevier, vol. 162(2), pages 248-267, June.
    3. Ye Li & Pierre Perron, 2017. "Inference on locally ordered breaks in multiple regressions," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 289-353, March.
    4. Kejriwal, Mohitosh & Perron, Pierre, 2008. "The limit distribution of the estimates in cointegrated regression models with multiple structural changes," Journal of Econometrics, Elsevier, vol. 146(1), pages 59-73, September.
    5. Pierre Perron & Yohei Yamamoto & Jing Zhou, 2020. "Testing jointly for structural changes in the error variance and coefficients of a linear regression model," Quantitative Economics, Econometric Society, vol. 11(3), pages 1019-1057, July.
    6. Seong Yeon Chang & Pierre Perron, 2018. "A comparison of alternative methods to construct confidence intervals for the estimate of a break date in linear regression models," Econometric Reviews, Taylor & Francis Journals, vol. 37(6), pages 577-601, July.
    7. Duan, Jiangtao & Bai, Jushan & Han, Xu, 2023. "Quasi-maximum likelihood estimation of break point in high-dimensional factor models," Journal of Econometrics, Elsevier, vol. 233(1), pages 209-236.
    8. Kejriwal, Mohitosh & Perron, Pierre, 2010. "Testing for Multiple Structural Changes in Cointegrated Regression Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 503-522.
    9. 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.
    10. Pierre Perron & Yohei Yamamoto, 2022. "Structural change tests under heteroskedasticity: Joint estimation versus two‐steps methods," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 389-411, May.
    11. Bai, Jushan & Duan, Jiangtao & Han, Xu, 2024. "The likelihood ratio test for structural changes in factor models," Journal of Econometrics, Elsevier, vol. 238(2).
    12. Yamamoto, Yohei & Tanaka, Shinya, 2015. "Testing for factor loading structural change under common breaks," Journal of Econometrics, Elsevier, vol. 189(1), pages 187-206.
    13. Pierre Perron & Yohei Yamamoto, 2015. "Using OLS to Estimate and Test for Structural Changes in Models with Endogenous Regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(1), pages 119-144, January.
    14. Karsten Schweikert, 2020. "Oracle Efficient Estimation of Structural Breaks in Cointegrating Regressions," Papers 2001.07949, arXiv.org, revised Apr 2021.
    15. Boldea, Otilia & Hall, Alastair R., 2013. "Estimation and inference in unstable nonlinear least squares models," Journal of Econometrics, Elsevier, vol. 172(1), pages 158-167.
    16. Baltagi, Badi H. & Feng, Qu & Kao, Chihwa, 2016. "Estimation of heterogeneous panels with structural breaks," Journal of Econometrics, Elsevier, vol. 191(1), pages 176-195.
    17. 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.
    18. Badi H. Baltagi & Qu Feng & Chihwa Kao, 2019. "Structural changes in heterogeneous panels with endogenous regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(6), pages 883-892, September.
    19. Mohitosh Kejriwal & Pierre Perron & Xuewen Yu, 2022. "A two‐step procedure for testing partial parameter stability in cointegrated regression models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 219-237, March.
    20. 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.

    More about this item

    Keywords

    Change-point; Segmented regressions; Break dates; Hypothesis testing; Multiple equations systems;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:204:y:2018:i:1:p:66-85. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.