Abstract
This is an overview paper, in which we briefly present results obtained over several years in the analysis, forecasting, and mining information from time series using methods that predominantly have nonstatistical character. Our main goal is to show the readers from the area of probability theory and statistics that nonstatistical methods can be pretty successful in time series processing. Besides the standard tasks such as estimation of trend/trend-cycle and forecasting, our methods are also powerful in providing additional information that can hardly be obtained using the statistical methods, namely, evaluation of the local course, finding perceptually important points, identification of structural breaks, finding periods of monotonous behavior including its evaluation, or summarization of information about large sets of time series. Our goal is not to beat statistical methods, but vice versa—to benefit from the synergy of both.
The work was supported from ERDF/ESF by the project “Centre for the development of Artificial Intelligence Methods for the Automotive Industry of the region” No. CZ.02.1.01/0.0/0.0/17-049/0008414.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The interval [0, 1] is a set of truth values where 0 means falsity, 1 truth, and the other values express partial truth. This interval can be replaced by a suitable bounded lattice.
- 2.
It has a good sense to speak about the probability of fuzzy events. For example, what is the probability that in the next few minutes, we will meet a tall woman.
- 3.
Such a function is implemented in the experimental software LFL Forecaster (see http://irafm.osu.cz/en/c110_lfl-forecaster/) developed in the Inst. for Research and Applications of Fuzzy Modeling of the University of Ostrava, Czech Republic, which implements the described methods. Its author is Viktor Pavliska. The results demonstrated in this paper were obtained using the mentioned software.
References
Anděl, J.: Statistical Analysis of Time Series. SNTL, Praha (1976 (in Czech))
Bovas, A., Ledolter, J.: Statistical Methods for Forecasting. Wiley, New York (2003)
Castillo-Ortega, R., Marín, N., Sánchez, D.: A fuzzy approach to the linguistic summarization of time series. Multiple Val. Logic Soft Comput. 17(2-3), 157–182 (2011)
De Wachter, S., Tzavalis, D.: Detection of structural breaks in linear dynamic panel data models. Computat. Stat. Data Anal. 56(11), 3020–3034 (2012)
Doerr, B., Fischer, P., Hilbert, A., Witt, C.: Detecting structural breaks in time series via genetic algorithms. Soft Computing 21(16), 4707–4720 (2017)
Dvořák, A., Holčapek, M.: L-fuzzy quantifiers of the type 〈1〉 determined by measures. Fuzzy Sets Syst. 160, 3425–3452 (2009)
Fu, T.C.: A review on time series data mining. Eng. Appl. Artif. Intell. 24, 164–181 (2011)
Hamilton, J.: Time Series Analysis. Princeton, Princeton University Press (1994)
Kacprzyk, J., Wilbik, A., Zadrożny, S.: Linguistic summarization of time series using a fuzzy quantifier driven aggregation. Fuzzy Sets Syst. 159, 1485–1499 (2008)
Kacprzyk, J., Wilbik, A., Zadrożny, S.: An approach to the linguistic summarization of time series using a fuzzy quantifier driven aggregation. Int. J. Intell. Syst. 25, 411–439 (2010)
Kreinovich, V., Perfilieva, I.: Fuzzy transforms of higher order approximate derivatives: A theorem. Fuzzy Sets Syst. 180, 55–68 (2011)
Mirshahi, S., Novák, V.: A fuzzy method for evaluating similar behaviour between assets. Soft Computing 25, 7813–7823 (2021)
Moyse, G., Lesot, M.: Linguistic summaries of locally periodic time series. Fuzzy Sets Syst. 285, 94–117 (2016)
Murinová, P., Novák, V.: A formal theory of generalized intermediate syllogisms. Fuzzy Sets Syst. 186, 47–80 (2012)
Murinová, P., Novák, V.: The structure of generalized intermediate syllogisms. Fuzzy Sets Syst. 247, 18–37 (2014)
Nguyen, L., Holčapek, M.: Suppression of high frequencies in time series using fuzzy transform of higher degree. In: Carvalho, J., et al. (eds.) Information Processing and Management of Uncertainty in Knowledge-Based Systems: 16th International Conference, IPMU 2016, vol. 2, pp. 705–716. Springer (2016)
Nguyen, L., Holčapek, M.: Higher degree fuzzy transform: Application to stationary processes and noise reduction. In: Kacprzyk, J., et al. (eds.) Advances in Fuzzy Logic and Technology 2017, vol. 3, pp. 1–12. Springer (2018)
Nguyen, L., Novák, V.: Filtering out high frequencies in time series using F-transform with respect to raised cosine generalized uniform fuzzy partition. In: Proc. Int. Conference FUZZ-IEEE 2015. IEEE Computer Society, CPS, Istanbul (2015)
Nguyen, L., Novák, V.: Trend-cycle forecasting based on new fuzzy techniques. In: Proc. Int. Conference FUZZ-IEEE 2017, pp. 1–6. Naples, Italy (2017)
Nguyen, L., Holčapek, M., Novák, V.: Multivariate fuzzy transform of complex-valued functions determined by monomial basis. Soft computing, 3641–3658 (2017)
Nguyen, L., Mirshahi, S., Novák, V.: Trend-cycle estimation using fuzzy transform and its application for identifying of bull and bear phases in markets. Intell. Syst. Account. Finance Manag. 27, 111–124 (2020). https://doi.org/10.1002/isaf.1473
Novák, V.: Perception-based logical deduction. In: Reusch, B. (ed.) Computational Intelligence, Theory and Applications, pp. 237–250. Springer, Berlin (2005)
Novák, V.: Mathematical fuzzy logic in modeling of natural language semantics. In: Wang, P., Ruan, D., Kerre, E. (eds.) Fuzzy Logic – A Spectrum of Theoretical & Practical Issues, pp. 145–182. Elsevier, Berlin (2007)
Novák, V.: A comprehensive theory of trichotomous evaluative linguistic expressions. Fuzzy Sets Syst. 159(22), 2939–2969 (2008)
Novák, V.: A formal theory of intermediate quantifiers. Fuzzy Sets Syst. 159(10), 1229–1246 (2008)
Novák, V.: Linguistic characterization of time series. Fuzzy Sets Syst. 285, 52–72 (2016)
Novák, V.: Mining information from time series in the form of sentences of natural language. Int. J. Approx. Reason. 78, 192–209 (2016)
Novák, V.: Detection of structural breaks in time series using fuzzy techniques. Int. J. Fuzzy Logic Intell. Syst. 18(1), 1–12 (2018)
Novák, V.: Fuzzy vs. probabilistic techniques in time series analysis. In: Anh, L., Dong, L., Kreinovich, V., Thach, N. (eds.) Econometrics for Financial Applications, pp. 213–234. Springer, Berlin (2018)
Novák, V., Lehmke, S.: Logical structure of fuzzy IF-THEN rules. Fuzzy Sets Syst. 157, 2003–2029 (2006)
Novák, V., Mirshahi, S.: On the similarity and dependence of time series. MDPI Mathematics 9(5), 550–563 (2021). https://doi.org/0.3390/math9050550. http://www.mdpi.com/2227-7390/9/5/550
Novák, V., Pavliska, V.: Time series: how unusual local behavior can be recognized using fuzzy modeling methods. In: Kreinovich, V. (ed.) Statistical and Fuzzy Approaches to Data Processing, with Applications to Econometrics and Other Areas, pp. 157–177. Springer, Berlin (2021)
Novák, V., Perfilieva, I.: On the semantics of perception-based fuzzy logic deduction. Int. J. Intell. Syst. 19, 1007–1031 (2004)
Novák, V., Perfilieva, I., Dvořák, A.: Insight into Fuzzy Modeling. Wiley, Hoboken, NJ (2016)
Novák, V., Perfilieva, I., Holčapek, M., Kreinovich, V.: Filtering out high frequencies in time series using F-transform. Information Sciences 274, 192–209 (2014)
Panigrahi, S., Behera, H.: Fuzzy time series forecasting: A survey. In: Behera, H., Nayak, J., Naik, B., Pelusi, D. (eds.) Computational Intelligence in Data Mining. pp. 641–651. Springer Singapore, Singapore (2020)
Perfilieva, I.: Fuzzy transforms: theory and applications. Fuzzy Sets Syst. 157, 993–1023 (2006)
Perfilieva, I., Adamczyk, D.: Features as keypoints and how fuzzy transforms retrieve them. In: Rojas, I., Joya, G., Català, A. (eds.) Advances in Computational Intelligence, IWANN 2021, vol. 12862. Springer, Cham (2021)
Perfilieva, I., Daňková, M., Bede, B.: Towards a higher degree F-transform. Fuzzy Sets Syst. 180, 3–19 (2011)
Preuss, P., Puchstein, R., Detter, H.: Detection of multiple structural breaks in multivariate time series. J. Am. Stat. Assoc. 110, 654–668 (2015)
Said, A., Taskaya-Temizel, T., Khurshid, A.: Summarizing time series: Learning patterns in ‘Volatile’ series. In: Yang, Z., Yin, H., Everson, R. (eds.) Intelligent Data Engineering and Automated Learning? IDEAL 2004, pp. 523–532. Lecture Notes in Computer Science. Springer, Berlin, Heidelberg (2004)
Song, Q., Chisom, B.: Forecasting enrollments with fuzzy time series - Part I. Fuzzy Sets Syst. 54, 1–9 (1993)
Štěpnička, M., Burda, M., Štěpničková, L.: Fuzzy rule base ensemble generated from data by linguistic associations mining. Fuzzy Sets Syst. 285, 140–161 (2016)
Truong, P., Novák, V.: An improved forecasting and detection of structural breaks in time series using fuzzy techniques. In: Rojas, I. (ed.) Contribution to Statistics. Springer (2022)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Novák, V., Perfilieva, I. (2023). Nonstatistical Methods for Analysis, Forecasting, and Mining Time Series. In: Valenzuela, O., Rojas, F., Herrera, L.J., Pomares, H., Rojas, I. (eds) Theory and Applications of Time Series Analysis and Forecasting. ITISE 2021. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-031-14197-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-031-14197-3_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-14196-6
Online ISBN: 978-3-031-14197-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)