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.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Box, G. E. P., & Jenkins, G. M. (1970). Time series analysis: Forecasting and control. San Francisco: Holden-Day.
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.
Chen, S. M. (2002). Forecasting enrollments based on high order fuzzy time series. Cybernetics and Systems, 33(1), 1–16.
Domańska, D., & Wojtylak, M. (2012). Application of fuzzy time series models for forecasting pollution concentrations. Expert Systems with Applications, 39(9), 7673–7679.
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.
Huarng, K. (2001). Effective lengths of intervals to improve forecasting in fuzzy time series. Fuzzy Sets and Systems, 123(3), 387–394.
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.
Lee, H. S., & Chou, M. T. (2014). Fuzzy forecasting based on fuzzy time series. International Journal of Computer Mathematics, 81, 781–789.
Lio, W., & Liu, B. (2018a). Uncertain data envelopment analysis with imprecisely observed inputs and outputs. Fuzzy Optimization and Decision Making, 17(3), 357–373.
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.
Liu, B. (2007). Uncertainty theory (2nd ed.). Berlin: Springer.
Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10.
Liu, B. (2010). Uncertainty theory: A branch of mathematics for modeling human uncertainty. Berlin: Springer.
Nejad, Z. M., & Ghaffari-Hadigheh, A. (2018). A novel DEA model based on uncertainty theory. Annals of Operations Research, 264, 367–389.
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.
Song, Q., & Chissom, B. S. (1993a). Forecasting enrollments with fuzzy time series: Part I. Fuzzy Sets and Systems, 54, 1–9.
Song, Q., & Chissom, B. S. (1993b). Fuzzy time series and its models. Fuzzy Sets and Systems, 54, 269–277.
Song, Q., & Chissom, B. S. (1994). Forecasting enrollments with fuzzy time series: Part II. Fuzzy Sets and Systems, 62, 1–8.
Sullivan, J., & Woodall, W. H. (1994). A comparison of fuzzy forecasting and Markov modeling. Fuzzy Sets and Systems, 64(3), 279–293.
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.
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.
Yao, K. (2018). Uncertain statistical inference models with imprecise observations. IEEE Transactions on Fuzzy Systems, 26(2), 409–415.
Yao, K., & Liu, B. (2018). Uncertain regression analysis: An approach for imprecise observations. Soft Computing, 22(17), 5579–5582.
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.
Walker, G. T. (1931). On periodicity in series of related terms. Proceedings of the Royal Society of London, Series A, 131, 518–532.
Acknowledgements
The authors gratefully acknowledge the financial support provided by National Natural Science Foundation of China (Grants Nos. 61573210 and 61873329).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yang, X., Liu, B. Uncertain time series analysis with imprecise observations. Fuzzy Optim Decis Making 18, 263–278 (2019). https://doi.org/10.1007/s10700-018-9298-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10700-018-9298-z