Korean Management Science Review (경영과학)

The Korean Operations Research and Management Science Society (한국경영과학회)
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Multi-scale Cluster Hierarchy for Non-stationary Functional Signals of Mutual Fund Returns

Mutual Fund 수익률의 비정상 함수형 시그널을 위한 다해상도 클러스터 계층구조

  • 김대룡 (동국대학교 경영학과) ;
  • 정욱 (동국대학교 경영학과)
  • Published : 2007.11.30
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Abstract

Many Applications of scientific research have coupled with functional data signal clustering techniques to discover novel characteristics that can be used for the diagnoses of several issues. In this article we present an interpretable multi-scale cluster hierarchy framework for clustering functional data using its multi-aspect frequency information. The suggested method focuses on how to effectively select transformed features/variables in unsupervised manner so that finally reduce the data dimension and achieve the multi-purposed clustering. Specially, we apply our suggested method to mutual fund returns and make superior-performing funds group based on different aspects such as global patterns, seasonal variations, levels of noise, and their combinations. To promise our method producing a quality cluster hierarchy, we give some empirical results under the simulation study and a set of real life data. This research will contribute to financial market analysis and flexibly fit to other research fields with clustering purposes.

Keywords

References

  1. Banfield, J.D. and A.E. Raftery, 'Modelbased Gaussian and non-gaussian clustering,' Biometrics, Vol.49(1993), pp.803-821 https://doi.org/10.2307/2532201
  2. Benz, C., P.D. Teresa, and R. Kinnel, Mutual Funds-Morningstar, John Wiley & Sons, 2003
  3. Calinski, T. and J. Harabasz, 'A dendrite method for cluster analysis,' Communications in Statistics, Vol.3, No.1(1974), pp.1-27
  4. Carreira-Perpinan, M., 'A review of dimension reduction techniques,' Technical report CS-96-09(1997), Department of Computer Science, University of Sheffield, UK]
  5. Donoho, D.L. and I.M. Johnstone, 'Adapting to unknown smoothness via wavelet shrinkage,' Journal of American Statistics Association, Vol.90(1995), pp.1200-1224 https://doi.org/10.2307/2291512
  6. Duda, R.O., P.E. Hart, and D.G. Stork, Pattern Classification, 2nd edn., Wiley, New York, NY, 2001
  7. Grogan, R. 'High speed stamping processimprovement thru force and displacement monitoring,' Technical report(2002), Helm Instrument Company, Maumee, OH
  8. Guyon, I. and A. Elissee, 'An introduction to variable and feature selection,' Journal of Machine Learning Research, Vol.3(2003), pp.1157-1182 https://doi.org/10.1162/153244303322753616
  9. Hartigan, J.A. Clustering Algorithms, New York, USA：John Wiley and Sons, 1975
  10. Hartigan, J.A. and Wong, M.A. 'A K-means clustering algorithm,' Applied Statistics, Vol.28, No.1(1978), pp.100-108
  11. Jensen, M.C., 'The performance of mutual funds in the period 1945-1964,' Journal of Finance Vol.23, No.2(1968), pp.389-416 https://doi.org/10.2307/2325404
  12. Jeong, M.K., J.C. Lu, X. Huo, B. Vidakovic, and D. Chen, 'Wavelet-based data reduction techniques for fault detection and classification,' Technometrics, Vol.48, No.1(2006), pp.26-40 https://doi.org/10.1198/004017005000000553
  13. Jin, J. and J. Shi, 'Automatic feature extraction of waveform signals for in-process diagnostic performance improvement,' Journal of Intelligent Manufacturing, Vol.12 (2001), pp.257-268 https://doi.org/10.1023/A:1011248925750
  14. Jung, U., M.K. Jeong, and J.C. Lu, 'A vertical-energy-thresholding procedure for data reduction with multiple complex curves,' IEEE Transactions on Systems, Man, and Cybernetics-Part B, Vol.36, No.5(2006a), pp.1128-1138 https://doi.org/10.1109/TSMCB.2006.874681
  15. Jung, U., M.K. Jeong, and J.C. Lu, 'Data reduction for multiple functional data with class information,' International Journal of Production Research, Vol.44, No14, 15(2006b), pp.2695-2710 https://doi.org/10.1080/00207540500539784
  16. Kaufman, L. and P. Rousseeuw, Finding Groups in Data：An Introduction to Cluster Analysis, New York：Wiley, 1990
  17. Kim, D.L., 'An empirical study of performance rating and distribution of mutual funds under the finite mixtures of normal distribution hypothesis,' Ph.D. dissertation, University of Nebraska, USA, 2003
  18. Krzanowski, W.J. and Y.T. Lai, 'A criterion for determining the number of groups in a data set using sum of squares clustering,' Biometrics, Vol.44, No.1(1988), pp.23-34 https://doi.org/10.2307/2531893
  19. Mallat, S.G., A Wavelet Tour of Signal Processing, Academic Press, San Diago,1989
  20. Ramsay, J., and B. Silverman, Functional Data Analysis, Springer Series in Statistics. Springer Verlag, 1997
  21. Rousseeuw, P.J., 'Silhouettes：a graphical aid to the interpretations and validation of cluster analysis,' Journal of Computational and Applied Mathematics, Vol.20(1987), pp. 53-65 https://doi.org/10.1016/0377-0427(87)90125-7
  22. Sharpe, W.F., 'Mutual fund performance,' Journal of Business Vol.39, No.1(1966), pp. 119-138 https://doi.org/10.1086/294846
  23. Sharpe, W.F., 'Morning star's risk-adjusted ratings,' Financial Analysis Journal, (1998), pp.21-33
  24. Treynor, J.L., 'How to rate management of investment funds,' Harvard Business Review, Vol.43, No.1(1965), pp.63-75
  25. Vidakovic, B., Statistical Modeling by Wavelets, John Wiley & Sons, 1999