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Detecting Structural Changes in Time Series by Using the BDS Test Recursively: An Application to COVID-19 Effects on International Stock Markets

Author

Listed:
  • Lorenzo Escot

    (Faculty of Statistical Studies, Complutense University of Madrid, Av. Puerta de Hierro 1, 28040 Madrid, Spain)

  • Julio E. Sandubete

    (Computing and Artificial Intelligence Lab, Universidad Camilo José Cela, c/Castillo de Alarcón, 49, 28691 Villanueva de la Cañada, Spain
    Faculty of Law, Business and Government, Universidad Francisco de Vitoria, Ctra. Pozuelo-Majadahonda Km 1,800, 28223 Pozuelo de Alarcón, Spain)

  • Łukasz Pietrych

    (Department of Statistics and Econometrics, Warsaw University of Life Sciences, Nowoursynowska 166, 02-787 Warszawa, Poland)

Abstract

Structural change tests aim to identify evidence of a structural break or change in the underlying generating process of a time series. The BDS test has its origins in chaos theory and seeks to test, using the correlation integral, the hypothesis that a time series is generated by an identically and independently distributed (IID) stochastic process over time. The BDS test is already widely used as a powerful tool for testing the hypothesis of white noise in the residuals of time series models. In this paper, we illustrate how the BDS test can be implemented also in a recursive manner to evaluate the hypothesis of structural change in a time series, taking advantage of its ability to test the IID hypothesis. We apply the BDS test repeatedly, starting with a sub-sample of the original time series and incrementally increasing the number of observations until it is applied to the full sample time series. A structural change in the unknown underlying generator model is detected when a change in the trend shown by this recursively computed BDS statistic is detected. The strength of this recursive BDS test lies in the fact that it does not require making any assumptions about the underlying time series generator model. We ilustrate the power and potential of this recursive BDS test through an application to real economic data. In this sense, we apply the test to assess the structural changes caused by the COVID-19 pandemic in international financial markets. Using daily data from the world’s top stock indices, we have detected strong and statistically significant evidence of two major structural changes during the period from June 2018 to June 2022. The first occurred in March 2020, coinciding with the onset of economic restrictions in the main Western countries as a result of the pandemic. The second occurred towards the end of August 2020, with the end of the main economic restrictions and the beginning of a new post-pandemic economic scenario. This methodology to test for structural changes in a time series is easy to implement and can detect changes in any system or process behind the time series even when this generating system is not known, and without the need to specify or estimate any a priori generating model. In this sense, the recursive BDS test could be incorporated as an initial preliminary step to any exercise of time series modeling. If a structural change is detected in a time series, rather than estimating a single predictive model for the full-sample time series, efforts should be made to estimate different predictive models, one for the time before and one for the time after the detected structural change.

Suggested Citation

  • Lorenzo Escot & Julio E. Sandubete & Łukasz Pietrych, 2023. "Detecting Structural Changes in Time Series by Using the BDS Test Recursively: An Application to COVID-19 Effects on International Stock Markets," Mathematics, MDPI, vol. 11(23), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4843-:d:1292558
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    References listed on IDEAS

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    1. Mariano Matilla-Garcia & Paloma Sanz & Francisco Vazquez, 2005. "The BDS test and delay time," Applied Economics Letters, Taylor & Francis Journals, vol. 12(2), pages 109-113.
    2. Muhammad Rehan & Jahanzaib Alvi & Süleyman Serdar Karaca, 2022. "Short Term Stress of Covid-19 on World Major Stock Indices," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 29(3), pages 527-568, September.
    3. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    4. Zeileis, Achim & Leisch, Friedrich & Hornik, Kurt & Kleiber, Christian, 2002. "strucchange: An R Package for Testing for Structural Change in Linear Regression Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 7(i02).
    5. Bhaskar Bagchi & Susmita Chatterjee & Raktim Ghosh & Dhrubaranjan Dandapat, 2020. "Coronavirus Outbreak and the Great Lockdown," SpringerBriefs in Economics, Springer, number 978-981-15-7782-6, October.
    6. 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.
    7. Omair Haroon & Syed Aun R. Rizvi, 2020. "Flatten the Curve and Stock Market Liquidity – An Inquiry into Emerging Economies," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 56(10), pages 2151-2161, August.
    8. 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.
    9. Lo, Andrew W. & Newey, Whitney K., 1985. "A large-sample chow test for the linear simultaneous equation," Economics Letters, Elsevier, vol. 18(4), pages 351-353.
    10. Dı́az, Andrés Fernández & Grau-Carles, Pilar & Mangas, Lorenzo Escot, 2002. "Nonlinearities in the exchange rates returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 469-482.
    11. Yarovaya, Larisa & Brzeszczyński, Janusz & Lau, Chi Keung Marco, 2016. "Intra- and inter-regional return and volatility spillovers across emerging and developed markets: Evidence from stock indices and stock index futures," International Review of Financial Analysis, Elsevier, vol. 43(C), pages 96-114.
    12. Christopher F Baum & Stan Hurn & Kenneth Lindsay, 2021. "The BDS test of independence," Stata Journal, StataCorp LP, vol. 21(2), pages 279-294, June.
    13. 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.
    14. Ligang Song & Yixiao Zhou, 2020. "The COVID‐19 Pandemic and Its Impact on the Global Economy: What Does It Take to Turn Crisis into Opportunity?," China & World Economy, Institute of World Economics and Politics, Chinese Academy of Social Sciences, vol. 28(4), pages 1-25, July.
    15. Hongxing Yao & Abdul Rashid Abdul Rahaman, 2018. "Efficient Market Hypothesis and the RMB-Dollar Rates: A Nonlinear Modeling of the Exchange Rate," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 10(2), pages 150-160, February.
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