Arbitrage Detection from Stock Data: An Empirical Study

Abstract

In this paper, we discuss the problems of arbitrage detection, which is known as change point detection in statistics. There are some classical methods for change point detection, such as the cumulative sum (CUSUM) procedure. However, when utilizing CUSUM, we must be sure about the model of the data before detecting. We introduce a new method to detect the change points by using Hilbert–Huang transformation (HHT) to devise a new algorithm. This new method (called the HHT test in this paper) has the advantage in that no model assumptions are required. Moreover, in some cases, the HHT test performs better than the CUSUM test, and has better simulation results. In the end, an empirical study of the volatility change based on the S&P 500 is also given for illustration.

Keywords

Arbitrage detection Hilbert–Huang transformation Volatility CUSUM 

References

  1. Huang, N. E. and S. P. Shen. 2005. Hilbert–Huang transform and its applications, World Scientific, London.Google Scholar
  2. Huang, N. E., Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Lin. 1998. “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis.” Proceedings of the Royal Society of London A 454, 903–995.Google Scholar
  3. Huang, N. E., M. C. Wu, S. R. Long, S. P. Shen, W. Qu, P. Gloersen, and K. L. Fan. 2003. “A confidence limit for the empirical mode decomposition and Hilbert spectral analysis.” Proceedings of the Royal Society of London A 459(2037), 2317–2345.CrossRefGoogle Scholar
  4. Page, E. S. 1954. “Continuous inspection schemes.” Biometrika 41, 100–115.Google Scholar
  5. Pollak, M. and Siegmund, D. 1985. “A diffusion process and its applications to detecting a change in the drift of Brownian motion.” Biometrika 72(2), 267–280.CrossRefGoogle Scholar
  6. Siegmund, D. 1985. Sequential analysis, Springer-Verlag, New York, NY.CrossRefGoogle Scholar
  7. Wu, Z. and Huang, N. E. 2004. “A study of characteristics of white noise using the empirical mode decomposition method.” Proceedings of the Royal Society of London 460, 1597–1611.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.National Central University and Academia SinicaTaipeiTaiwan
  2. 2.National Taiwan UniversityTaipeiTaiwan

Personalised recommendations