IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v198y2023ics0047259x23000568.html
   My bibliography  Save this article

Testing for changes in linear models using weighted residuals

Author

Listed:
  • Horváth, Lajos
  • Rice, Gregory
  • Zhao, Yuqian

Abstract

We study methods for detecting change points in linear regression models. Motivated by statistics arising from maximally selected likelihood ratio tests, we provide an asymptotic theory for weighted functionals of the cumulative sum (CUSUM) process of linear model residuals. Special attention is given to standardized quadratic form statistics, leading to Darling–Erdős type limit results, as well as novel heavily weighted CUSUM statistics that increase the power of the tests to detect changes that occur early or late in the sample. We discuss improved finite-sample approaches to estimate the critical values for the proposed statistics, which are shown to work well in a Monte Carlo simulation study. The proposed tests are applied to the environmental Kuznets curve, and a COVID-19 dataset.

Suggested Citation

  • Horváth, Lajos & Rice, Gregory & Zhao, Yuqian, 2023. "Testing for changes in linear models using weighted residuals," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:jmvana:v:198:y:2023:i:c:s0047259x23000568
    DOI: 10.1016/j.jmva.2023.105210
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X23000568
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2023.105210?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Lajos Horváth & Gregory Rice, 2014. "Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 219-255, June.
    2. Klaus Frick & Axel Munk & Hannes Sieling, 2014. "Multiscale change point inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(3), pages 495-580, June.
    3. Harchaoui, Z. & Lévy-Leduc, C., 2010. "Multiple Change-Point Estimation With a Total Variation Penalty," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1480-1493.
    4. Grossman, G.M & Krueger, A.B., 1991. "Environmental Impacts of a North American Free Trade Agreement," Papers 158, Princeton, Woodrow Wilson School - Public and International Affairs.
    5. Alexander Aue & Lajos Horváth, 2013. "Structural breaks in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 1-16, January.
    6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    7. Jiang, Feiyu & Zhao, Zifeng & Shao, Xiaofeng, 2023. "Time series analysis of COVID-19 infection curve: A change-point perspective," Journal of Econometrics, Elsevier, vol. 232(1), pages 1-17.
    8. Gombay, Edit, 2008. "Change detection in autoregressive time series," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 451-464, March.
    9. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    10. Shahbaz, Muhammad & Sinha, Avik, 2019. "Environmental Kuznets Curve for CO2 emission: A survey of empirical literature," MPRA Paper 100257, University Library of Munich, Germany, revised 2019.
    11. 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.
    12. Axel Bücher & Jean‐David Fermanian & Ivan Kojadinovic, 2019. "Combining Cumulative Sum Change‐Point Detection Tests for Assessing the Stationarity of Univariate Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(1), pages 124-150, January.
    13. Eiji Kurozumi, 2018. "Confidence Sets for the Date of a Structural Change at the End of a Sample," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 850-862, November.
    14. Gombay, Edit & Horváth, Lajos, 1994. "Limit theorems for change in linear regression," Journal of Multivariate Analysis, Elsevier, vol. 48(1), pages 43-69, January.
    15. Liu, Weidong & Wu, Wei Biao, 2010. "Asymptotics Of Spectral Density Estimates," Econometric Theory, Cambridge University Press, vol. 26(4), pages 1218-1245, August.
    16. Shi, Xuesheng & Gallagher, Colin & Lund, Robert & Killick, Rebecca, 2022. "A comparison of single and multiple changepoint techniques for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 170(C).
    17. Fryzlewicz, Piotr, 2014. "Wild binary segmentation for multiple change-point detection," LSE Research Online Documents on Economics 57146, London School of Economics and Political Science, LSE Library.
    18. Lajos Horváth & Gregory Rice, 2014. "Rejoinder on: Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 287-290, June.
    19. Lajos Horváth & Curtis Miller & Gregory Rice, 2020. "A New Class of Change Point Test Statistics of Rényi Type," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 570-579, July.
    Full references (including those not matched with items on IDEAS)

    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. Pouliot, William, 2016. "Robust tests for change in intercept and slope in linear regression models with application to manager performance in the mutual fund industry," Economic Modelling, Elsevier, vol. 58(C), pages 523-534.
    2. Lajos Horváth & Curtis Miller & Gregory Rice, 2021. "Detecting early or late changes in linear models with heteroscedastic errors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 577-609, June.
    3. Zifeng Zhao & Feiyu Jiang & Xiaofeng Shao, 2022. "Segmenting time series via self‐normalisation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1699-1725, November.
    4. Claudia Kirch & Christina Stoehr, 2022. "Sequential change point tests based on U‐statistics," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1184-1214, September.
    5. Kleiber, Christian, 2016. "Structural Change in (Economic) Time Series," Working papers 2016/06, Faculty of Business and Economics - University of Basel.
    6. Holger Dette & Dominik Wied, 2016. "Detecting relevant changes in time series models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 371-394, March.
    7. Bouzebda, Salim & Ferfache, Anouar Abdeldjaoued, 2023. "Asymptotic properties of semiparametric M-estimators with multiple change points," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    8. Horváth, Lajos & Liu, Zhenya & Rice, Gregory & Wang, Shixuan, 2020. "Sequential monitoring for changes from stationarity to mild non-stationarity," Journal of Econometrics, Elsevier, vol. 215(1), pages 209-238.
    9. Lajos Horváth & William Pouliot & Shixuan Wang, 2017. "Detecting at-Most-m Changes in Linear Regression Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(4), pages 552-590, July.
    10. Bill Russell & Dooruj Rambaccussing, 2019. "Breaks and the statistical process of inflation: the case of estimating the ‘modern’ long-run Phillips curve," Empirical Economics, Springer, vol. 56(5), pages 1455-1475, May.
    11. Alaa Abi Morshed & Elena Andreou & Otilia Boldea, 2018. "Structural Break Tests Robust to Regression Misspecification," Econometrics, MDPI, vol. 6(2), pages 1-39, May.
    12. Fabrizio Ghezzi & Eduardo Rossi & Lorenzo Trapani, 2024. "Fast Online Changepoint Detection," Papers 2402.04433, arXiv.org.
    13. Lee, Taewook & Baek, Changryong, 2020. "Block wild bootstrap-based CUSUM tests robust to high persistence and misspecification," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    14. 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.
    15. Florian Pein & Hannes Sieling & Axel Munk, 2017. "Heterogeneous change point inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1207-1227, September.
    16. Cui, Junfeng & Wang, Guanghui & Zou, Changliang & Wang, Zhaojun, 2023. "Change-point testing for parallel data sets with FDR control," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    17. Jiang, Feiyu & Wang, Runmin & Shao, Xiaofeng, 2023. "Robust inference for change points in high dimension," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    18. Federico A. Bugni & Jia Li & Qiyuan Li, 2023. "Permutation‐based tests for discontinuities in event studies," Quantitative Economics, Econometric Society, vol. 14(1), pages 37-70, January.
    19. Jiang, Feiyu & Zhao, Zifeng & Shao, Xiaofeng, 2023. "Time series analysis of COVID-19 infection curve: A change-point perspective," Journal of Econometrics, Elsevier, vol. 232(1), pages 1-17.
    20. Mohamed Salah Eddine Arrouch & Echarif Elharfaoui & Joseph Ngatchou-Wandji, 2023. "Change-Point Detection in the Volatility of Conditional Heteroscedastic Autoregressive Nonlinear Models," Mathematics, MDPI, vol. 11(18), pages 1-31, September.

    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:jmvana:v:198:y:2023:i:c:s0047259x23000568. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.