Comparison of Time Series via Classic and Temporal Protoforms of Linguistic Summaries: An Application to Mutual Funds and Their Benchmarks
Conference paper
Abstract
We present a new approach to the evaluation of similarity of time series that are characterized by linguistic summaries. We consider so-called temporal data summaries, i.e. novel linguistic summaries that explicitly include a temporal aspect. We consider the case of a mutual (investment) fund and its underlying benchmark(s), and the new comparison method is based not on the comparison of the consecutive values or segments of the fund and its benchmark but on the comparison of classic and temporal linguistic summaries (i.e. based on a classic and temporal protoform) best describing their past behavior.
Keywords
Time series comparison Linguistic data summarization Temporal protoform Fuzzy logic Computing with wordsPreview
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References
- 1.Agrawal, R., Faloutsos, C., Swami, A.: Efficient similarity search in sequence databases. In: Lomet, D.B. (ed.) FODO 1993. LNCS, vol. 730, pp. 69–84. Springer, Heidelberg (1993)Google Scholar
- 2.Chan, K.P., Fu, W.C.: Efficient time series matching by wavelets. In: Proceedings of the 15th International Conference on Data Engineering, ICDE 1999, Sydney, Austrialia, p. 126. IEEE Computer Society, Los Alamitos (1999)Google Scholar
- 3.Chiu, B., Keogh, E., Lonardi, S.: Probabilistic discovery of time series motifs. In: Proceedings of the the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 493–498 (2003)Google Scholar
- 4.Cross, V., Sudkamp, T.: Similarity and Compatibility in Fuzzy Set Theory: Assessment and Applications. Springer, Heidelberg (2002)MATHGoogle Scholar
- 5.Das, G., Gunopulos, D., Mannila, H.: Finding similar time series. In: Komorowski, J., Żytkow, J.M. (eds.) PKDD 1997. LNCS, vol. 1263, pp. 88–100. Springer, Heidelberg (1997)Google Scholar
- 6.Geurts, P.: Pattern extraction for time series classification. In: Siebes, A., De Raedt, L. (eds.) PKDD 2001. LNCS (LNAI), vol. 2168, p. 115. Springer, Heidelberg (2001)CrossRefGoogle Scholar
- 7.Kacprzyk, J., Fedrizzi, M.: ’Soft’ consensus measures for monitoring real consensus reaching processes under fuzzy preferences. Control Cybernet 15, 309–323 (1986)MathSciNetGoogle Scholar
- 8.Kacprzyk, J., Fedrizzi, M.: A ’soft‘ measure of consensus in the setting of partial (fuzzy) preferences. European J. Oper. Res. 34, 315–325 (1988)CrossRefMathSciNetGoogle Scholar
- 9.Kacprzyk, J., Fedrizzi, M.: A ’human-consistent‘ degree of consensus based on fuzzy logic with linguistic quantifiers. Math. Social Sci. 18, 275–290 (1989)MATHCrossRefMathSciNetGoogle Scholar
- 10.Kacprzyk, J., Fedrizzi, M., Nurmi, H.: Group decision making and consensus under fuzzy preferences and fuzzy majority. Fuzzy Sets Syst. 49, 21–31 (1992)MATHCrossRefMathSciNetGoogle Scholar
- 11.Kacprzyk, J., Wilbik, A.: Using fuzzy linguistic summaries for the comparison of time series: an application to the analysis of investment fund quotations. In: Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, IFSA/EUSFLAT 2009, Lisbon, Portugal, pp. 1321–1326 (2009)Google Scholar
- 12.Kacprzyk, J., Wilbik, A.: A comprehensive comparison of time series described by linguistic summaries and its application to the analysis of performance of a mutual fund and its benchmark. In: Proceedings of the 2010 World Conference on Computational Intelligence, WCCI 2010, Barcelona, Spain (in press, 2010)Google Scholar
- 13.Kacprzyk, J., Wilbik, A.: Temporal linguistic summaries of time series using fuzzy logic. In: Proceedings of International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2010, Dortmund, Germany (in press, 2010)Google Scholar
- 14.Kacprzyk, J., Yager, R.R.: Linguistic summaries of data using fuzzy logic. Int. J. Gen. Syst. 30, 33–154 (2001)CrossRefMathSciNetGoogle Scholar
- 15.Kacprzyk, J., Zadrożny, S.: Linguistic database summaries and their protoforms: toward natural language based knowledge discovery tools. Inform. Sci. 173, 281–304 (2005)CrossRefMathSciNetGoogle Scholar
- 16.Kacprzyk, J., Zadrożny, S.: Towards a general and unified characterization of individual and collective choice functions under fuzzy and nonfuzzy preferences and majority via the ordered weighted average operators. Int. J. Intell. Syst. 24(1), 4–26 (2009)MATHCrossRefGoogle Scholar
- 17.Kacprzyk, J., Zadrożny, S.: Computing with words is an implementable paradigm: fuzzy queries, linguistic data summaries and natural language generation. IEEE Trans. Fuzzy Syst. (to appear, 2010)Google Scholar
- 18.Kacprzyk, J., Yager, R.R., Zadrożny, S.: A fuzzy logic based approach to linguistic summaries of databases. Int. J. Appl. Math. Comput. Sci. 10, 813–834 (2000)MATHGoogle Scholar
- 19.Kacprzyk, J., Wilbik, A., Zadrożny, S.: Linguistic summarization of time series under different granulation of describing features. In: Kryszkiewicz, M., Peters, J.F., Rybiński, H., Skowron, A. (eds.) RSEISP 2007. LNCS (LNAI), vol. 4585, pp. 230–240. Springer, Heidelberg (2007)CrossRefGoogle Scholar
- 20.Keogh, E., Ratanamahatana, C.A.: Exact indexing of dynamic time warping. Knowl. Inform. Syst. 7(3), 358–386 (2005)CrossRefGoogle Scholar
- 21.Keogh, E., Chakrabarti, K., Pazzani, M., Mehrotra, S.: Locally adaptive dimensionality reduction for indexing large time series databases. In: Proceedings of ACM SIGMOD Conference on Management of Data, Santa Barbara, CA, pp. 151–162 (2001)Google Scholar
- 22.Keogh, E., Chu, S., Hart, D., Pazzani, M.: Segmenting time series: A survey and novel approach. In: Data Mining in Time Series Databases, World Scientific Publishing, Singapore (2004)Google Scholar
- 23.Mueen, A., Keogh, E., Zhu, Q., Cash, S., Westover, B.: Exact discovery of time series motifs. In: Proceedings of the SIAM International Conference on Data Mining, SDM 2009, Sparks, Nevada, USA, pp. 473–484 (2009)Google Scholar
- 24.Yager, R.R.: A new approach to the summarization of data. Inform. Sci. 28, 69–86 (1982)MATHCrossRefMathSciNetGoogle Scholar
- 25.Zadeh, L.A.: Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst. 9(2), 111–127 (1983)MathSciNetGoogle Scholar
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