Abstract
Uncertain time series is a method to predict future values based on previously uncertain observed values, which is firstly proposed by Yang and Liu (Fuzzy Optim Decis Mak, 2019. https://doi.org/10.1007/s10700-018-9298-z). This paper continues to study a special uncertain time series—uncertain autoregressive model, and gives an analytic solution of uncertain autoregressive model based on the principle of least squares. Moreover, this paper proves another equivalent form to calculate the unknown parameters of uncertain autoregressive model via uncertainty distribution and also analyzes the disturbance term via uncertainty distribution.
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References
Fang L, Hong Y (2019) Uncertain revised regression analysis with responses of logarithmic, square root and reciprocal transformations. Soft Comput. https://doi.org/10.1007/s00500-019-03821-x
Feng Y, Dai L, Gao J (2019) Uncertain pursuit-evasion game. Soft Comput. https://doi.org/10.1007/s00500-018-03689-3
Hu Z, Gao J (2019) Uncertain Gompertz regression model with imprecise observations. Soft Comput. https://doi.org/10.1007/s00500-018-3611-1
Gao J (2013) Uncertain bimatrix game with applications. Fuzzy Optim Decis Mak 12(1):65–78
Gao J, Yang X, Liu D (2017) Uncertain Shapley value of coalitional game with application to supply chain alliance. Appl Soft Comput 56:551–556
Jiang B, Lio W, Li X (2019a) An uncertain DEA model for scale efficiency evaluation. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2018.2883546
Jiang B, Li Y, Lio W, Li J (2019b) Sustainability efficiency evaluation of seaports in China: an uncertain data envelopment analysis approach. Soft Comput. https://doi.org/10.1007/s00500-018-3559-1
Lio W, Liu B (2018a) Uncertain data envelopment analysis with imprecisely observed inputs and outputs. Fuzzy Optim Decis Mak 17(3):357–373
Lio W, Liu B (2018b) Residual and confidence interval for uncertain regression model with imprecise observations. J Intell Fuzzy Syst 35(2):2573–2583
Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin
Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10
Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, Berlin
Liu B (2015) Uncertainty theory, 4th edn. Springer, Berlin
Liu Z, Yang Y (2019) Least absolute deviations estimation for uncertain regression with imprecise observations. Fuzzy Optim Decis Mak (to be published)
Mohmmad NZ, Ghaffari-Hadigheh A (2018) A novel DEA model based on uncertainty theory. Ann Oper Res 264:367–389
Song Y, Fu Z (2018) Uncertain multivariable regression model. Soft Comput 22(17):5861–5866
Wang Y, Luo S, Gao J (2017) Uncertain extensive game with application to resource allocation of national security. J Ambient Intell Hum Comput 8(5):797–808
Wen ML (2015) Uncertain data envelopment analysis. Springer, Berlin
Wen ML, Guo LH, Kang R, Yang Y (2014) Data envelopment analysis with uncertain inputs and outputs. J Appl Math. https://doi.org/10.1155/2014/307108
Yang X, Gao J (2013) Uncertain differential games with application to capitalism. J Uncertain Anal Appl 1:17
Yang X, Gao J (2014) Uncertain core for coalitional game with uncertain payoffs. J Uncertain Syst 8(2):13–21
Yang X, Gao J (2016) Linear-quadratic uncertain differential games with application to resource extraction problem. IEEE Trans Fuzzy Syst 24(4):819–826
Yang X, Gao J (2017) Bayesian equilibria for uncertain bimatrix game with asymmetric information. J Intell Manuf 28(3):515–525
Yang X, Liu B (2019) Uncertain time series analysis with imprecise observations. Fuzzy Optim Decis Mak. https://doi.org/10.1007/s10700-018-9298-z
Yao K (2018) Uncertain statistical inference models with imprecise observations. IEEE Trans Fuzzy Syst 26(2):409–415
Yao K, Liu B (2018) Uncertain regression analysis: an approach for imprecise observations. Soft Comput 22(17):5579–5582
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This work is supported by the National Natural Science Foundation (No. 61873108) of China.
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Zhao, X., Peng, J., Liu, J. et al. Analytic solution of uncertain autoregressive model based on principle of least squares. Soft Comput 24, 2721–2726 (2020). https://doi.org/10.1007/s00500-019-04128-7
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DOI: https://doi.org/10.1007/s00500-019-04128-7