Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
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On the Estimation Techniques of Hurst exponent

허스트 지수 산정 방법에 대한 고찰

  • 김병식 (한국건설기술연구원 수자원연구부) ;
  • 김형수 (인하대학교 토목공학과) ;
  • 서병하 (인하대학교 토목공학과)
  • Published : 2004.12.01
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Abstract

There are many different techniques for the estimation of the Hurst exponent. However, the techniques can produce different characteristics for the persistence of a time series each other. This study uses several techniques such as adjusted range, resealed range(RR) analysis, modified restated range(MRR) analysis, 1/f power spectral density analysis, Maximum Likelihood Estimation(MLE), detrended fluctuations analysis(DFA), and aggregated variance time(AVT)method for the Hurst exponent estimation. The generated time series from chaos and stochastic systems are analyzed for the comparative study of the techniques. Then this study discusses the advantages and disadvantages of the techniques and also the limitations of them.

허스트 지수를 산정하기 위하여 기존에 여러 방법론들이 제안되어 왔다. 그러나, 이들 방법론들은 시계열들의 지속성에 대하여 각기 다른 특성들을 보이고 있음을 기존의 연구에서 알 수 있다 따라서 본 연구에서는 수문학에서 주로 이용하고 있는 보정용량, 조정용량, 수정조정용량 방법 이외에 생리학 분야와 전자 분야 등에서 이용되고 있는 1/f 파워 스펙트럼 밀도 분석, DFA, AVT 방법, 최우도법 등을 이용하여 허스트 지수를 산정하여 보았다. 즉, 단기간과 장기간 기억을 가진 카오스와 추계학적 시계열들에 대하여 각각의 방법들을 적용하여 비교 분석하고자 하였으며, 각 방법론들에 대한 장점 및 단점 그리고 한계에 대하여 논의하였다.

Keywords

References

  1. 김형수, 박진욱, 김중훈 (1998). '수문 시계열의 Hurst 현상.', 대한토목학회논문집, 대한토목학회, 제 18권, 제II-6호, pp. 571-582
  2. Ausloos, M. A. (2000). 'Statistical Physics in foreign exchange currency and stock markets.', Physica A, Vol. 285, pp. 48-65 https://doi.org/10.1016/S0378-4371(00)00271-5
  3. Bigger, T., Richard, C., Steinman, A.B., Linda, M., Joseph, L., and Richard, J. (1996). 'Power law behavior of RR-interval variability in healthy middle-aged persons, patients with recent acute myocardial infarction, and patients with heart transplants.', Circulation. Vol. 93, pp. 2142-2151 https://doi.org/10.1161/01.CIR.93.12.2142
  4. Goldberger, A.L., Amaral, L.A.N., Hausdorff, J.M., Ivanov, P.C., Peng, CK., and Stanley, H.E. (2002). 'Fractal dynamics in physiology; Alterations with disease and aging.', PANS., Vol. 99., pp. 2466-2472 https://doi.org/10.1073/pnas.012579499
  5. Herman, P. (1999). 'Physiological time series; distinguishing fractal noises from motions.', European Journal of Physiology, Vol. 439, pp. 403-415 https://doi.org/10.1007/s004240050957
  6. Hipel, K.W. and Mcleod, A.I. (1994). 'Time series modelling of water resources and environmental system', Elsevier Science, Amsterdam
  7. Hurst, H. (1951). 'Long-term storage capacity of reservoirs.', Transcation of the American Society of Civil engineer, Vol. 116, pp. 770-799
  8. Kantelhardt, J.W., Koscielny, B.E., Rego, H.A., Havlin, S., and Bunde, A. (2001). 'Detecting long range correlations with Detrended Fluctuation Analysis.', Physica A Vol. 295, pp. 441 https://doi.org/10.1016/S0378-4371(01)00144-3
  9. Kashyap, R.L. and Rao, A.R. (1976). 'Modeling river flows.', Dynamic stochastic models from empirical data, Academic, New York, pp. 238-281
  10. Kendziorski, C.M. (1999). 'Evaluation maximum likeihood estimation methods to determine the Hurst coefficient', Physica A Vol. 273 pp. 439-451 https://doi.org/10.1016/S0378-4371(99)00268-X
  11. Lo, A.W. (1991). 'Long term memory in stock market prices.', Economtrica, Vol. 59, pp. 1279-1313 https://doi.org/10.2307/2938368
  12. Mandelbrot, B. and Wallis, J. (1969). 'Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence.', Water Resour. Res., Vol. 5, pp. 967-988 https://doi.org/10.1029/WR005i005p00967
  13. Nakamura, Y., Yamamoto, Y., and Muraoka, I. (1993). ' Autonomic control of heart rate during physical exercise and fractal dimension of heart rate variability. J Appl Physiol., Vol. 74, pp. 875-881
  14. Pallikari, F. (1999). 'Rescaled Range Analysis of Random Events.', Journal of scientific Exploration, Vol. 13, pp. 25-40
  15. Philips, P. (1987). 'Time series regression with a unit roof.' Econometrica., Vol. 55, pp. 703-705 https://doi.org/10.2307/1913237
  16. Rao, A.R. and Bhattacharya, D. (1999). 'Hypothesis testing for long term memory in hydrologic series.', Journal of Hydrology., Vol. 216, pp. 183-196 https://doi.org/10.1016/S0022-1694(99)00005-0
  17. Rao, A.R. and Bhattacharya, D. (2001). 'Effect of short-term memory on hurst phenomenon.', Journal of Hydrologic Engineering. March/April, pp. 125-131 https://doi.org/10.1061/(ASCE)1084-0699(2001)6:2(125)
  18. MathSoft (2000). S-Plus2000 ; Guide to statistical and mathematical analysis. StatSci Dvision, Seattle, Washinton
  19. Salas, J. D., Delleur, J. W., Yevjevich, V., and Lane, W. L. (1995). 'Applied modelling of hydrologic time series' WRP
  20. Taqqu, M.S., and Teverovsky, V. (1995). 'Estimation for long range dependence; an empirical study.', Fractals, Vol. 3(4), pp. 785-798 https://doi.org/10.1142/S0218348X95000692
  21. Teverovsky, V., Taqqu, M.S., and Willinger, W. (1998). 'Acritical look at Lo's modified R/S statistic.', Journal of Statistical Planning and Inference https://doi.org/10.1016/S0378-3758(98)00250-X
  22. Tong, H.(l990).'Non-linear Time Series; ADynamical System Approach.' Clarendon press oxford
  23. Zafer, S. and Sirin, T. (1999). 'Traffic engineering for multimedia networks; data collection onthe internet, extensions to wireless.', NSF industry/University co-operative research center for digital video & media
  24. Zhao, Y. (1998). 'Self-similarity in high performance network analysis.', University of missouri-Columbia

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