A Novel FRBF-Type Model for Nonlinear Time Series Prediction

Table 2

Statistical results of the FRBF-ARX model with various structures for the testing data and comparison of computing time for training data.

No.	Model	Structure	Time (s)	RMSE	NMSE
1	ARX	(2, 1)	3.381	46.143	0.514
	FRBF-ARX	(2, 1, 2, 2, 2)	6.858	39.857	0.444
2	ARX	(2, 2)	4.027	46.147	0.514
	FRBF-ARX	(2, 2, 4, 4, 2)	8.414	40.178	0.448
3	ARX	(3, 1)	4.052	44.194	0.492
	FRBF-ARX	(3, 1, 4, 4, 2)	10.669	40.499	0.451
4	ARX	(3, 2)	4.029	44.192	0.492
	FRBF-ARX	(3, 2, 6, 6, 2)	13.449	41.044	0.457
5	ARX	(3, 3)	4.057	44.195	0.492
	FRBF-ARX	(3, 3, 6, 6, 2)	14.971	41.572	0.463
6	ARX	(4, 1)	4.073	44.338	0.494
	FRBF-ARX	(4, 1, 6, 6, 2)	12.671	41.731	0.465
7	ARX	(4, 2)	4.049	44.334	0.494
	FRBF-ARX	(4, 2, 6, 6, 2)	14.755	41.592	0.463
8	ARX	(4, 3)	4.023	44.338	0.494
	FRBF-ARX	(4, 3, 6, 6, 2)	25.432	43.269	0.482
9	ARX	(4, 4)	4.001	44.342	0.494
	FRBF-ARX	(4, 4, 6, 6, 2)	13.731	40.482	0.451
10	ARX	(5, 1)	4.025	44.336	0.493
	FRBF-ARX	(5, 1, 6, 6, 2)	10.869	40.445	0.451
11	ARX	(5, 2)	4.031	44.333	0.493
	FRBF-ARX	(5, 2, 6, 6, 2)	8.418	43.304	0.482
12	ARX	(5, 3)	4.033	44.334	0.493
	FRBF-ARX	(5, 3, 8, 8, 2)	23.637	41.923	0.467
13	ARX	(5, 4)	4.042	44.343	0.493
	FRBF-ARX	(5, 4, 9, 9, 2)	23.907	42.131	0.469
14	ARX	(5, 5)	3.973	44.344	0.493
	FRBF-ARX	(5, 5, 9, 9, 2)	25.344	42.384	0.472