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Testing for changes in linear models using weighted residuals

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  • 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
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    References listed on IDEAS

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    1. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    2. 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.
    3. 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.
    4. 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.
    5. Gombay, Edit & Horváth, Lajos, 1994. "Limit theorems for change in linear regression," Journal of Multivariate Analysis, Elsevier, vol. 48(1), pages 43-69, January.
    6. 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.
    7. Alexander Aue & Lajos Horváth, 2013. "Structural breaks in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 1-16, January.
    8. Liu, Weidong & Wu, Wei Biao, 2010. "Asymptotics Of Spectral Density Estimates," Econometric Theory, Cambridge University Press, vol. 26(4), pages 1218-1245, August.
    9. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    10. 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.
    11. Gombay, Edit, 2008. "Change detection in autoregressive time series," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 451-464, March.
    12. 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.
    13. 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).
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    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.
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