DOI QR코드

DOI QR Code

A Multi-Resolution Approach to Non-Stationary Financial Time Series Using the Hilbert-Huang Transform

  • 발행 : 2009.06.30

초록

An economic signal in the real world usually reflects complex phenomena. One may have difficulty both extracting and interpreting information embedded in such a signal. A natural way to reduce complexity is to decompose the original signal into several simple components, and then analyze each component. Spectral analysis (Priestley, 1981) provides a tool to analyze such signals under the assumption that the time series is stationary. However when the signal is subject to non-stationary and nonlinear characteristics such as amplitude and frequency modulation along time scale, spectral analysis is not suitable. Huang et al. (1998b, 1999) proposed a data-adaptive decomposition method called empirical mode decomposition and then applied Hilbert spectral analysis to decomposed signals called intrinsic mode function. Huang et al. (1998b, 1999) named this two step procedure the Hilbert-Huang transform(HHT). Because of its robustness in the presence of nonlinearity and non-stationarity, HHT has been used in various fields. In this paper, we discuss the applications of the HHT and demonstrate its promising potential for non-stationary financial time series data provided through a Korean stock price index.

키워드

참고문헌

  1. Alexandrov, T. (2008). A method of trend extraction using singular spectrum analysis, ArXiv e-prints, 804. URL http://arxiv.org/abs/0804.3367v2
  2. Boasnash, B. (1992). Estimating and interpreting the instantaneous frequency of a signal-part 1: Fundamentals, Proceedinqs of The IEEE, 80, 520-538
  3. Cohen, L (1995). Time-Frequency Analysis, Prentice-Hall, Englewood Cliffs
  4. Coughlin, K. T. and Tung, K. K. (2004). 11-year solar cycle in the stratosphere extracted by the empirical mode decomposition method, Advances in Space Research, 34, 323-329 https://doi.org/10.1016/j.asr.2003.02.045
  5. Deering, R. and Kaiser, J. F. (2005). The use of a masking signal to improve empirical mode decomposition, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 4, 485-488
  6. Flandrin, P., Rilling, G. and Goncalves, P. (2004). Empirical mode decomposition as a filter bank, IEEE Signal Processing Letters, 11, 112-114 https://doi.org/10.1109/LSP.2003.821662
  7. Huang, N. E., Shen, Z. and Long, S. R. (1999). A new view of nonlinear water waves: The Hilbert spectrum, Annual Review of Fluid Mechanics, 31, 417-457 https://doi.org/10.1146/annurev.fluid.31.1.417
  8. Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N. C., Tung, C. C. and Liu, H. H. (1998b). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proceedings of the Royal Society, London, A454, 903-995 https://doi.org/10.1098/rspa.1998.0193
  9. Huang, N. E., Wu, M. L. C., Long, S. R., Shen, S. S. P., Qu, W., Gloersen, P. and Fan, K. L. (2003a). A confidence limit for the empirical mode decomposition and Hilbert spectral analysis, Proceedings of the Royal Society London, A459, 2317-2345 https://doi.org/10.1098/rspa.2003.1123
  10. Huang, N. E., Wu, M. L. C., Qu, W., Long, S. R., Shen, S. S. P. and Zhang, J. E. (2003b). Applications of Hilbert-Huang transform to non-stationary financial time series analysis, Applied Stochastic Models in Business and Industry, 19, 245-268 https://doi.org/10.1002/asmb.501
  11. Huang, W., Shen, Z., Huang, N. E. and Fung, Y. C. (1998a). Use of intrinsic modes in biology: Examples of indicial response of pulmonary blood pressure to $\pm$ step hypoxia, Proceedinqs of the National Academic of Sciences of the United States of America, 95, 12766-12771 https://doi.org/10.1073/pnas.95.22.12766
  12. Huang, W., Sher, Y. P., Peck, K. and Fung, Y. C. (2002). Matching gene activity with physiological functions, Proceedings of the National Academic of Sciences of the United States of America, 99, 2603-2608 https://doi.org/10.1073/pnas.042684399
  13. Kim, D. and Oh, H. S. (2006). Hierarchical smoothing technique by empirical mode decomposition, The Korean Journal of Applied Statistics, 19, 319-330 https://doi.org/10.5351/KJAS.2006.19.2.319
  14. Kim, D. and Oh, H. S. (2008). EMD: Empirical Mode Decomposition and Hilbert Spectral Analysis, URL http://cran.r-project.org/web/packages/EMD/index.html
  15. Kim, D., Paek, S. H. and Oh, H. S. (2008). A Hilbert-Huang transform approach for predicting cyber-attacks, Journal of the Korean Statistical Society, 37, 277-283 https://doi.org/10.1016/j.jkss.2008.02.006
  16. Liu, Z. F., l.iao, Z. P. and Sang, E. F. (2005). Speech enhancement based on Hilbert-Huang transform, Proceedings of 2005 International Conference on Machine Learning and Cybernetics, 8, 4908-4912
  17. Mallat, S. G. (1998). A Wavelet Tour of Signal Processing, Academic Press, San Diego
  18. Priestley, M. B. (1981). Spectral Analysis and Time Series, Academic Press, New York
  19. Rilling, G., Flandrin, P. and Goncalves, P. (2003). On empirical mode decomposition and its algorithm, Proceedings of the IEEE-EURASIP Workshop on Nonlinear Signal an d Image Processing, NSIP03
  20. Zeng, K. and He, M. X. (2004). A simple boundary process technique for empirical mode decomposition, Proceedings of 2004 IEEE International Geoscience and Remote Sensing Symposium, 6, 4258-4261 https://doi.org/10.1109/IGARSS.2004.1370076
  21. Zhang, R. R., Ma, S., Safak, E. and Hartzell, S. (2003). Hilbert-Huang transform analysis of dynamic and earthquake motion recordings, Journal of Engineering Mechanics, 129, 861-875 https://doi.org/10.1061/(ASCE)0733-9399(2003)129:8(861)

피인용 문헌

  1. A Hilbert-Huang Transform Approach Combined with PCA for Predicting a Time Series vol.24, pp.6, 2011, https://doi.org/10.5351/KJAS.2011.24.6.995
  2. EMD based hybrid models to forecast the KOSPI vol.29, pp.3, 2016, https://doi.org/10.5351/KJAS.2016.29.3.525
  3. Impact Tension Damage Mechanism Analyses of Co-Woven-Knitted Composite from Hilbert–Huang Transform vol.21, pp.4, 2012, https://doi.org/10.1177/1056789511406759
  4. Empirical Mode Decomposition using the Second Derivative vol.26, pp.2, 2013, https://doi.org/10.5351/KJAS.2013.26.2.335