American Institute of Mathematical Sciences

September  2020, 10(3): 355-366. doi: 10.3934/naco.2020007

An improved ARMA(1, 1) type fuzzy time series applied in predicting disordering

 1 Department of Basic, Shenyang University of Technology, Liaoyang, 111000, China, Department of Mathematics, Northeastern University, Shenyang, 110004, China 2 Department of Mathematics, Northeastern University, Shenyang, 110004, China

* Corresponding author: Tie Zhang

Received  May 2019 Revised  October 2019 Published  February 2020

Fund Project: This work is supported by the State Key Laboratory of Synthetical Automation for Process Industries Fundamental Research Funds, No. 2013ZCX02

Fuzzy time series shows great advantages in dealing with incomplete or unreasonable data. But most of them are based on fuzzy AR time series model, so it is necessary to add MA variables to the fuzzy time series [10] to make it more accurate. An improved ARMA(1, 1) type fuzzy time series based on fuzzy logic group relations including fuzzy MA variables along with fuzzy AR variables was proposed in this paper. To take full account of the errors, the prediction errors were added to the forecast fuzzy sets, and it made the first-order fuzzy logical relationship sets more exact. In order to verify the advantage of the proposed method, it was applied to predict the stock prices of State Bank of India (SBI) and the packet disordering from a common source host in the Northeast University to www. yahoo. com. The experimental results showed that the proposed model was more precise than other models.

Citation: Zhi Liu, Tie Zhang. An improved ARMA(1, 1) type fuzzy time series applied in predicting disordering. Numerical Algebra, Control & Optimization, 2020, 10 (3) : 355-366. doi: 10.3934/naco.2020007
References:

show all references

References:
A comparison between the proposed model and other models
A comparison between the proposed model and other models
A comparison between the delays of the proposed model and the real delays
Example of weights.
 Time FLR Weight $\; t=1$ $A_i \rightarrow A_j$ 1 $\; t=2$ $A_i \rightarrow A_k$ 1 $\; t=3$ $A_i \rightarrow A_j$ 1 $\; t=4$ $A_i \rightarrow A_l$ 1 $\; t=5$ $A_i \rightarrow A_j$ 1
 Time FLR Weight $\; t=1$ $A_i \rightarrow A_j$ 1 $\; t=2$ $A_i \rightarrow A_k$ 1 $\; t=3$ $A_i \rightarrow A_j$ 1 $\; t=4$ $A_i \rightarrow A_l$ 1 $\; t=5$ $A_i \rightarrow A_j$ 1
The predication values.
 Year Actual price The rate of change PRC Predicted $t$ (in rupee) $r(t)\%$ values 6/5/2012 2080.25 6/6/2012 2159.45 3.81 3.81 6/7/2012 2167.85 0.39 0.38 2167.66 6/8/2012 2180.05 0.56 0.61 2181.07 6/11/2012 2164.55 -0.71 -0.65 2165.88 6/12/2012 2206.90 1.96 1.91 2205.89 6/13/2012 2222.25 0.70 0.68 2221.91 6/14/2012 2154.25 -3.06 -3.12 2152.92 6/15/2012 2182.80 1.33 0.99 2175.58 6/18/2012 2087.65 -4.36 -4.36 2087.63 ⋮ ⋮ ⋮ ⋮ ⋮ 7/17/2012 2198.85 0.20 0.16 2197.96 7/18/2012 2185.95 -0.57 -0.65 2184.56 7/19/2012 2157.75 -1.29 -1.29 2157.75 7/20/2012 2134.55 -1.08 -1.03 2135.53 7/23/2012 2092.55 -1.97 -1.96 2092.71 7/24/2012 2094.80 0.11 0.09 2094.43 7/25/2012 2070.65 -1.15 -1.03 2073.22 7/26/2012 2017.15 -2.58 -2.40 2020.95 7/27/2012 1941.20 -3.77 -3.74 1941.71 7/31/2012 2005.20 3.30 3.36 2006.42
 Year Actual price The rate of change PRC Predicted $t$ (in rupee) $r(t)\%$ values 6/5/2012 2080.25 6/6/2012 2159.45 3.81 3.81 6/7/2012 2167.85 0.39 0.38 2167.66 6/8/2012 2180.05 0.56 0.61 2181.07 6/11/2012 2164.55 -0.71 -0.65 2165.88 6/12/2012 2206.90 1.96 1.91 2205.89 6/13/2012 2222.25 0.70 0.68 2221.91 6/14/2012 2154.25 -3.06 -3.12 2152.92 6/15/2012 2182.80 1.33 0.99 2175.58 6/18/2012 2087.65 -4.36 -4.36 2087.63 ⋮ ⋮ ⋮ ⋮ ⋮ 7/17/2012 2198.85 0.20 0.16 2197.96 7/18/2012 2185.95 -0.57 -0.65 2184.56 7/19/2012 2157.75 -1.29 -1.29 2157.75 7/20/2012 2134.55 -1.08 -1.03 2135.53 7/23/2012 2092.55 -1.97 -1.96 2092.71 7/24/2012 2094.80 0.11 0.09 2094.43 7/25/2012 2070.65 -1.15 -1.03 2073.22 7/26/2012 2017.15 -2.58 -2.40 2020.95 7/27/2012 1941.20 -3.77 -3.74 1941.71 7/31/2012 2005.20 3.30 3.36 2006.42
MSE of different methods.
 Errors [4] [18] [16] Proposed model RMSE 54.1958 82.3197 32.2586 1.6498
 Errors [4] [18] [16] Proposed model RMSE 54.1958 82.3197 32.2586 1.6498
 [1] Chuang Peng. Minimum degrees of polynomial models on time series. Conference Publications, 2005, 2005 (Special) : 720-729. doi: 10.3934/proc.2005.2005.720 [2] Ruiqi Li, Yifan Chen, Xiang Zhao, Yanli Hu, Weidong Xiao. Time series based urban air quality predication. Big Data & Information Analytics, 2016, 1 (2&3) : 171-183. doi: 10.3934/bdia.2016003 [3] Yu-Ting Lin, John Malik, Hau-Tieng Wu. Wave-shape oscillatory model for nonstationary periodic time series analysis. Foundations of Data Science, 2021, 3 (2) : 99-131. doi: 10.3934/fods.2021009 [4] Yung Chung Wang, Jenn Shing Wang, Fu Hsiang Tsai. Analysis of discrete-time space priority queue with fuzzy threshold. Journal of Industrial & Management Optimization, 2009, 5 (3) : 467-479. doi: 10.3934/jimo.2009.5.467 [5] Ahmad Deeb, A. Hamdouni, Dina Razafindralandy. Comparison between Borel-Padé summation and factorial series, as time integration methods. Discrete & Continuous Dynamical Systems - S, 2016, 9 (2) : 393-408. doi: 10.3934/dcdss.2016003 [6] Cheng Peng, Zhaohui Tang, Weihua Gui, Qing Chen, Jing He. A bidirectional weighted boundary distance algorithm for time series similarity computation based on optimized sliding window size. Journal of Industrial & Management Optimization, 2021, 17 (1) : 205-220. doi: 10.3934/jimo.2019107 [7] Hassan Khodaiemehr, Dariush Kiani. High-rate space-time block codes from twisted Laurent series rings. Advances in Mathematics of Communications, 2015, 9 (3) : 255-275. doi: 10.3934/amc.2015.9.255 [8] Annalisa Pascarella, Alberto Sorrentino, Cristina Campi, Michele Piana. Particle filtering, beamforming and multiple signal classification for the analysis of magnetoencephalography time series: a comparison of algorithms. Inverse Problems & Imaging, 2010, 4 (1) : 169-190. doi: 10.3934/ipi.2010.4.169 [9] Hongbiao Fan, Jun-E Feng, Min Meng. Piecewise observers of rectangular discrete fuzzy descriptor systems with multiple time-varying delays. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1535-1556. doi: 10.3934/jimo.2016.12.1535 [10] Chao Wang, Zhien Li, Ravi P. Agarwal. Hyers-Ulam-Rassias stability of high-dimensional quaternion impulsive fuzzy dynamic equations on time scales. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021041 [11] Editorial Office. Retraction: Xiao-Qian Jiang and Lun-Chuan Zhang, Stock price fluctuation prediction method based on time series analysis. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 915-915. doi: 10.3934/dcdss.2019061 [12] Armengol Gasull, Francesc Mañosas. Subseries and signed series. Communications on Pure & Applied Analysis, 2019, 18 (1) : 479-492. doi: 10.3934/cpaa.2019024 [13] Omid S. Fard, Javad Soolaki, Delfim F. M. Torres. A necessary condition of Pontryagin type for fuzzy fractional optimal control problems. Discrete & Continuous Dynamical Systems - S, 2018, 11 (1) : 59-76. doi: 10.3934/dcdss.2018004 [14] Bernard Ducomet. Asymptotics for 1D flows with time-dependent external fields. Conference Publications, 2007, 2007 (Special) : 323-333. doi: 10.3934/proc.2007.2007.323 [15] Yuusuke Sugiyama. Degeneracy in finite time of 1D quasilinear wave equations Ⅱ. Evolution Equations & Control Theory, 2017, 6 (4) : 615-628. doi: 10.3934/eect.2017031 [16] Jiaquan Zhan, Fanyong Meng. Cores and optimal fuzzy communication structures of fuzzy games. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1187-1198. doi: 10.3934/dcdss.2019082 [17] Xiaodong Liu, Wanquan Liu. The framework of axiomatics fuzzy sets based fuzzy classifiers. Journal of Industrial & Management Optimization, 2008, 4 (3) : 581-609. doi: 10.3934/jimo.2008.4.581 [18] Juan J. Nieto, M. Victoria Otero-Espinar, Rosana Rodríguez-López. Dynamics of the fuzzy logistic family. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 699-717. doi: 10.3934/dcdsb.2010.14.699 [19] Natalia Skripnik. Averaging of fuzzy integral equations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : 1999-2010. doi: 10.3934/dcdsb.2017118 [20] Purnima Pandit. Fuzzy system of linear equations. Conference Publications, 2013, 2013 (special) : 619-627. doi: 10.3934/proc.2013.2013.619

Impact Factor: