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

Table 6

Data set 2 forecasts and forecasting performances for the best results of the methods with the sample size 15 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
11.12.2009	49386	49271,7	48950	49250	49600	49100	49569,5	49300	49984	49516	49250
14.12.2009	50198	49791	48950	49250	49600	49300	49569,5	49100	49984	50064	50150
15.12.2009	50450	50139,3	50450	50150	49866,7	50500	50222,5	50500	49984	50942	50150
16.12.2009	50817	50139,3	50450	51050	49866,7	48900	49796	51300	49984	50217	50450
17.12.2009	49963	50171	50450	50150	50400	50900	50736,6	50500	49984	49641	50450
18.12.2009	50138	50068,7	50450	51050	49600	49900	50222,5	50100	49984	49619	50450
21.12.2009	51281	50068,7	50450	51050	49866,7	50500	50222,5	50500	49984	50932	50450
22.12.2009	51533	50333,9	51200	51050	50400	50966,7	50882,5	51100	49984	50817	51350
23.12.2009	51162	51121	51200	51350	50400	51500	50882,5	51500	49984	51100	51050
24.12.2009	51461	50333,9	50450	51350	50400	50550	50882,5	50500	49984	50646	51050
25.12.2009	51661	51121	51200	51200	50400	51500	50882,5	51500	49984	51073	51650
28.12.2009	51619	51121	51200	51500	52000	51700	51776,2	51900	49984	51117	51350
29.12.2009	51786	51121	51200	51800	52000	51700	51776,2	51900	49984	51114	51650
30.12.2009	51668	50741	51200	51950	52000	51700	51776,2	51900	49984	51119	51350
31.12.2009	52825	51121	51200	51950	52000	51700	51776,2	51900	49984	51117	51650
RMSE		804,45	713,35	471,49	803,72	760,77	623,27	553,84	1381,68	662,35	451,53
MAPE		0,0126	0,0112	0,0072	0,0140	0,0110	0,0099	0,0085	0,0225	0,0106	0,0066
DA		0,4286	0,5000	0,6429	0,3571	0,5000	0,6429	0,6429	0,4286	0,5000	0,7143

^*The best result.