Skip to main content
Erschienen in: Fuzzy Optimization and Decision Making 3/2019

28.11.2018

Uncertain time series analysis with imprecise observations

verfasst von: Xiangfeng Yang, Baoding Liu

Erschienen in: Fuzzy Optimization and Decision Making | Ausgabe 3/2019

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Time series analysis is a method to predict future values based on previously observed values. Assuming the observed values are imprecise and described by uncertain variables, this paper proposes an approach of uncertain time series. By employing the principle of least squares, a minimization problem is derived to calculate the unknown parameters in the uncertain time series model. In addition, residual and confidence interval are also proposed. Finally, some numerical examples are given.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Box, G. E. P., & Jenkins, G. M. (1970). Time series analysis: Forecasting and control. San Francisco: Holden-Day.MATH Box, G. E. P., & Jenkins, G. M. (1970). Time series analysis: Forecasting and control. San Francisco: Holden-Day.MATH
Zurück zum Zitat Cai, Q., Zhang, D., Zheng, W., & Leung, S. C. (2015). A new fuzzy time series forecasting model combined with ant colony optimization and auto-regression. Knowledge-Based Systems, 74, 61–68.CrossRef Cai, Q., Zhang, D., Zheng, W., & Leung, S. C. (2015). A new fuzzy time series forecasting model combined with ant colony optimization and auto-regression. Knowledge-Based Systems, 74, 61–68.CrossRef
Zurück zum Zitat Chen, S. M. (2002). Forecasting enrollments based on high order fuzzy time series. Cybernetics and Systems, 33(1), 1–16.CrossRefMATH Chen, S. M. (2002). Forecasting enrollments based on high order fuzzy time series. Cybernetics and Systems, 33(1), 1–16.CrossRefMATH
Zurück zum Zitat Domańska, D., & Wojtylak, M. (2012). Application of fuzzy time series models for forecasting pollution concentrations. Expert Systems with Applications, 39(9), 7673–7679.CrossRef Domańska, D., & Wojtylak, M. (2012). Application of fuzzy time series models for forecasting pollution concentrations. Expert Systems with Applications, 39(9), 7673–7679.CrossRef
Zurück zum Zitat Egrioglu, E., Yolcu, U., Aladag, C. H., & Kocak, C. (2013). An ARMA type fuzzy time series forecasting method based on particle swarm optimization. Mathematical Problems in Engineering, 2013, Article ID 935815. Egrioglu, E., Yolcu, U., Aladag, C. H., & Kocak, C. (2013). An ARMA type fuzzy time series forecasting method based on particle swarm optimization. Mathematical Problems in Engineering, 2013, Article ID 935815.
Zurück zum Zitat Huarng, K. (2001). Effective lengths of intervals to improve forecasting in fuzzy time series. Fuzzy Sets and Systems, 123(3), 387–394.MathSciNetCrossRefMATH Huarng, K. (2001). Effective lengths of intervals to improve forecasting in fuzzy time series. Fuzzy Sets and Systems, 123(3), 387–394.MathSciNetCrossRefMATH
Zurück zum Zitat Lee, L. W., Wang, L. H., Chen, S. M., & Leu, Y. H. (2006). Handling forecasting problems based on two-factors high-order fuzzy time series. IEEE Transactions on Fuzzy Systems, 14(3), 468–477.CrossRef Lee, L. W., Wang, L. H., Chen, S. M., & Leu, Y. H. (2006). Handling forecasting problems based on two-factors high-order fuzzy time series. IEEE Transactions on Fuzzy Systems, 14(3), 468–477.CrossRef
Zurück zum Zitat Lee, H. S., & Chou, M. T. (2014). Fuzzy forecasting based on fuzzy time series. International Journal of Computer Mathematics, 81, 781–789.MathSciNetCrossRefMATH Lee, H. S., & Chou, M. T. (2014). Fuzzy forecasting based on fuzzy time series. International Journal of Computer Mathematics, 81, 781–789.MathSciNetCrossRefMATH
Zurück zum Zitat Lio, W., & Liu, B. (2018a). Uncertain data envelopment analysis with imprecisely observed inputs and outputs. Fuzzy Optimization and Decision Making, 17(3), 357–373.MathSciNetCrossRefMATH Lio, W., & Liu, B. (2018a). Uncertain data envelopment analysis with imprecisely observed inputs and outputs. Fuzzy Optimization and Decision Making, 17(3), 357–373.MathSciNetCrossRefMATH
Zurück zum Zitat Lio, W., & Liu, B. (2018b). Residual and confidence interval for uncertain regression model with imprecise observations. Journal of Intelligent and Fuzzy Systems, 35(1), 2573–2583.CrossRef Lio, W., & Liu, B. (2018b). Residual and confidence interval for uncertain regression model with imprecise observations. Journal of Intelligent and Fuzzy Systems, 35(1), 2573–2583.CrossRef
Zurück zum Zitat Liu, B. (2007). Uncertainty theory (2nd ed.). Berlin: Springer.MATH Liu, B. (2007). Uncertainty theory (2nd ed.). Berlin: Springer.MATH
Zurück zum Zitat Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10. Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10.
Zurück zum Zitat Liu, B. (2010). Uncertainty theory: A branch of mathematics for modeling human uncertainty. Berlin: Springer.CrossRef Liu, B. (2010). Uncertainty theory: A branch of mathematics for modeling human uncertainty. Berlin: Springer.CrossRef
Zurück zum Zitat Nejad, Z. M., & Ghaffari-Hadigheh, A. (2018). A novel DEA model based on uncertainty theory. Annals of Operations Research, 264, 367–389.MathSciNetCrossRefMATH Nejad, Z. M., & Ghaffari-Hadigheh, A. (2018). A novel DEA model based on uncertainty theory. Annals of Operations Research, 264, 367–389.MathSciNetCrossRefMATH
Zurück zum Zitat Sheng, Y. H., & Kar, S. (2015). Some results of moments of uncertain variable through inverse uncertainty distribution. Fuzzy Optimization and Decision Making, 14(1), 57–76.MathSciNetCrossRefMATH Sheng, Y. H., & Kar, S. (2015). Some results of moments of uncertain variable through inverse uncertainty distribution. Fuzzy Optimization and Decision Making, 14(1), 57–76.MathSciNetCrossRefMATH
Zurück zum Zitat Song, Q., & Chissom, B. S. (1993a). Forecasting enrollments with fuzzy time series: Part I. Fuzzy Sets and Systems, 54, 1–9.CrossRef Song, Q., & Chissom, B. S. (1993a). Forecasting enrollments with fuzzy time series: Part I. Fuzzy Sets and Systems, 54, 1–9.CrossRef
Zurück zum Zitat Song, Q., & Chissom, B. S. (1994). Forecasting enrollments with fuzzy time series: Part II. Fuzzy Sets and Systems, 62, 1–8.CrossRef Song, Q., & Chissom, B. S. (1994). Forecasting enrollments with fuzzy time series: Part II. Fuzzy Sets and Systems, 62, 1–8.CrossRef
Zurück zum Zitat Sullivan, J., & Woodall, W. H. (1994). A comparison of fuzzy forecasting and Markov modeling. Fuzzy Sets and Systems, 64(3), 279–293.CrossRef Sullivan, J., & Woodall, W. H. (1994). A comparison of fuzzy forecasting and Markov modeling. Fuzzy Sets and Systems, 64(3), 279–293.CrossRef
Zurück zum Zitat Tseng, F. M., Tzeng, G. H., Yu, H. C., & Yuan, B. J. C. (2001). Fuzzy ARIMA model for forecasting the foreign exchange market. Fuzzy Sets and Systems, 118(1), 9–19.MathSciNetCrossRef Tseng, F. M., Tzeng, G. H., Yu, H. C., & Yuan, B. J. C. (2001). Fuzzy ARIMA model for forecasting the foreign exchange market. Fuzzy Sets and Systems, 118(1), 9–19.MathSciNetCrossRef
Zurück zum Zitat Wen, M. L., Zhang, Q. Y., Kang, R., & Yang, Y. (2017). Some new ranking criteria in data envelopment analysis under uncertain environment. Computers and Industrial Engineering, 110, 498–504.CrossRef Wen, M. L., Zhang, Q. Y., Kang, R., & Yang, Y. (2017). Some new ranking criteria in data envelopment analysis under uncertain environment. Computers and Industrial Engineering, 110, 498–504.CrossRef
Zurück zum Zitat Yao, K. (2018). Uncertain statistical inference models with imprecise observations. IEEE Transactions on Fuzzy Systems, 26(2), 409–415.CrossRef Yao, K. (2018). Uncertain statistical inference models with imprecise observations. IEEE Transactions on Fuzzy Systems, 26(2), 409–415.CrossRef
Zurück zum Zitat Yao, K., & Liu, B. (2018). Uncertain regression analysis: An approach for imprecise observations. Soft Computing, 22(17), 5579–5582.CrossRefMATH Yao, K., & Liu, B. (2018). Uncertain regression analysis: An approach for imprecise observations. Soft Computing, 22(17), 5579–5582.CrossRefMATH
Zurück zum Zitat Yule, G. U. (1927). On a method of investigating periodicities in disturbed series with special reference to Wolfer’s sunspot numbers. Philosophical Transactions of the Royal Society of London, 226, 267–298.CrossRefMATH Yule, G. U. (1927). On a method of investigating periodicities in disturbed series with special reference to Wolfer’s sunspot numbers. Philosophical Transactions of the Royal Society of London, 226, 267–298.CrossRefMATH
Zurück zum Zitat Walker, G. T. (1931). On periodicity in series of related terms. Proceedings of the Royal Society of London, Series A, 131, 518–532.CrossRefMATH Walker, G. T. (1931). On periodicity in series of related terms. Proceedings of the Royal Society of London, Series A, 131, 518–532.CrossRefMATH
Metadaten
Titel
Uncertain time series analysis with imprecise observations
verfasst von
Xiangfeng Yang
Baoding Liu
Publikationsdatum
28.11.2018
Verlag
Springer US
Erschienen in
Fuzzy Optimization and Decision Making / Ausgabe 3/2019
Print ISSN: 1568-4539
Elektronische ISSN: 1573-2908
DOI
https://doi.org/10.1007/s10700-018-9298-z

Weitere Artikel der Ausgabe 3/2019

Fuzzy Optimization and Decision Making 3/2019 Zur Ausgabe

Premium Partner