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

- Journal title : Korean Journal of Applied Statistics
- Volume 22, Issue 3, 2009, pp.499-513
- Publisher : The Korean Statistical Society
- DOI : 10.5351/KJAS.2009.22.3.499

Title & Authors

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

Oh, Hee-Seok; Suh, Jeong-Ho; Kim, Dong-Hoh;

Oh, Hee-Seok; Suh, Jeong-Ho; Kim, Dong-Hoh;

Abstract

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.

Keywords

Empirical mode decomposition;Hilbert-Huang transform;Hilbert spectral analysis;multi-resolution analysis;non-stationarity;

Language

English

Cited by

1.

A Hilbert-Huang Transform Approach Combined with PCA for Predicting a Time Series,;

1.

2.

3.

References

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

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

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

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

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

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

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

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

13.

Kim, D. and Oh, H. S. (2006). Hierarchical smoothing technique by empirical mode decomposition, The Korean Journal of Applied Statistics, 19, 319-330

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

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