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Detection of changes in a random financial sequence with a stable distribution

Author

Listed:
  • Dong Han
  • Fugee Tsung
  • Yanting Li
  • Jinguo Xian

Abstract

Quick detection of unanticipated changes in a financial sequence is a critical problem for practitioners in the finance industry. Based on refined logarithmic moment estimators for the four parameters of a stable distribution, this article presents a stable-distribution-based multi-CUSUM chart that consists of several CUSUM charts and detects changes in the four parameters in an independent and identically distributed random sequence with the stable distribution. Numerical results of the average run lengths show that the multi-CUSUM chart is superior (robust and quick) on the whole to a single CUSUM chart in detecting the shift change of the four parameters. A real example that monitors changes in IBM's stock returns is used to demonstrate the performance of the proposed method.

Suggested Citation

  • Dong Han & Fugee Tsung & Yanting Li & Jinguo Xian, 2010. "Detection of changes in a random financial sequence with a stable distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(7), pages 1089-1111.
    • Handle: RePEc:taf:japsta:v:37:y:2010:i:7:p:1089-1111
    DOI: 10.1080/02664760902914433
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    References listed on IDEAS

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    1. Liu, Shi-Miin & Brorsen, B Wade, 1995. "Maximum Likelihood Estimation of a Garch-Stable Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(3), pages 273-285, July-Sept.
    2. Carmela Quintos & Zhenhong Fan & Peter C. B. Phillips, 2001. "Structural Change Tests in Tail Behaviour and the Asian Crisis," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(3), pages 633-663.
    3. Bruce E. Hansen, 2001. "The New Econometrics of Structural Change: Dating Breaks in U.S. Labour Productivity," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 117-128, Fall.
    4. JosE Fajardo & Ernesto Mordecki, 2006. "Symmetry and duality in Levy markets," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 219-227.
    5. Loretan, Mico & Phillips, Peter C. B., 1994. "Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets," Journal of Empirical Finance, Elsevier, vol. 1(2), pages 211-248, January.
    6. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    7. 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.
    8. Alwan, Layth C & Roberts, Harry V, 1988. "Time-Series Modeling for Statistical Process Control," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(1), pages 87-95, January.
    9. Samuelson, Paul A., 1967. "Efficient Portfolio Selection for Pareto-Lévy Investments*," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(2), pages 107-122, June.
    10. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    11. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2003. "A theory of power-law distributions in financial market fluctuations," Nature, Nature, vol. 423(6937), pages 267-270, May.
    12. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Josep Lluís Carrion-i-Silvestre & Andreu Sansó, 2023. "“Generalized Extreme Value Approximation to the CUMSUMQ Test for Constant Unconditional Variance in Heavy-Tailed Time Series”," AQR Working Papers 202305, University of Barcelona, Regional Quantitative Analysis Group, revised Jul 2023.
    2. Qu, Liang & Wu, Zhang & Khoo, Michael B.C. & Castagliola, Philippe, 2013. "A CUSUM scheme for event monitoring," International Journal of Production Economics, Elsevier, vol. 145(1), pages 268-280.

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