A New High Order Fuzzy ARMA Time Series Forecasting Method by Using Neural Networks to Define Fuzzy Relations

Table 7

Data set 3 forecasts and forecasting performances for the best results of the methods with the sample size 7 for the test data.

Date	IMKB	Song-Chissom method [1]	Chen method [5]	Chen method [14]	Huarng distribution-based method [6]	Huarng average-based method [6]	Huarng ratio-based method [8]	Aladag et al. method [18]	Cheng et al. method [9]	Yolcu et al. method [25]	^*Proposed method
15.12.2010	65499	65356	66550	65900,0	67400	66500	66784,7	67300	65992	65999	65350
16.12.2010	64429	65356	66250	65900,0	65400	66300	66178,0	64900	65992	64813	64450
17.12.2010	63524	65975	64450	64800,0	65900	64500	65878,7	64900	65992	64864	64450
20.12.2010	63502	64737	63550	64066,7	64900	63500	63514,3	64300	65992	64871	63550
21.12.2010	64820	64737	63550	63700,0	64900	63500	63514,3	63700	65992	64858	64450
22.12.2010	65440	65975	65800	64800,0	65900	65500	65878,7	65500	65992	65522	65350
23.12.2010	66219	65356	66250	65900,0	65400	66300	66178,0	66700	65992	64813	66250
RMSE		1161,91	1001,70	928,70	1365,14	1014,73	1317,77	1034,06	1544,90	929,82	383,29
MAPE		0,0139	0,0122	0,0128	0,0177	0,0118	0,0159	0,0135	0,0200	0,0113	0,0036
DA		0,50000	0,50000	0,33333	0,50000	0,50000	0,66667	0,66667	0,5000	0,5000	0,6667

^*The best result.