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

Zhi Liu; Tie Zhang

doi:10.3934/naco.2020007

Article Contents

2020, Volume 10, Issue 3: 355-366. Doi: 10.3934/naco.2020007

This issue Previous Article Sliding mode control for uncertain T-S fuzzy systems with input and state delays Next Article Fault estimation and optimization for uncertain disturbed singularly perturbed systems with time-delay

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

Zhi Liu^1,2, and
Tie Zhang^2, ,

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
^* Corresponding author: Tie Zhang

Received: May 2019

Revised: October 2019

Published: June 2020

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

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Abstract

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.

Keywords:

Fuzzy time series; ARMA(1,
1) type fuzzy time series; packet disordering.

Mathematics Subject Classification: 62A86.

Citation:

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Figure 1. A comparison between the proposed model and other models

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Figure 2. A comparison between the proposed model and other models

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Figure 3. A comparison between the delays of the proposed model and the real delays

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Table 1. 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

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Table 2. 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

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Table 3. MSE of different methods.

Errors	[4]	[18]	[16]	Proposed model
RMSE	54.1958	82.3197	32.2586	1.6498

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