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

Table 3

Data set 1 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
23.12.2008	26294	26411,5	26400	26200	26666,7	26100	26708,8	26200	26390	26274	26200
24.12.2008	26055	26411,5	26400	26200	26666,7	26366,7	26708,8	26200	26390	26273	26200
25.12.2008	26059	26411,5	26400	26200	26666,7	26100	26708,8	26200	26390	26339	26200
26.12.2008	26499	26411,5	26400	26200	26666,7	26100	26708,8	26200	26390	26337	26600
29.12.2008	26424	26411,5	26600	26400	26666,7	26500	26708,8	26600	26390	26565	26600
30.12.2008	26411	26411,5	26600	26533,3	26666,7	26500	26708,8	26600	26390	26429	26600
31.12.2008	26864	26411,5	26600	26600	26666,7	26500	26708,8	26600	26390	26460	26600
RMSE		261,24	236,87	179,04	391,62	251,24	424,20	198,40	258,87	219,27	167,48
MAPE		0,0075	0,0083	0,0059	0,0134	0,0080	0,0145	0,0071	0,0076	0,0067	0,0060
DA		0,8333	0,5000	0,8333	0,5000	0,5000	0,5000	0,6667	0,6667	0,6667	0,6667

^*The best result.