Forecasting Using Information and Entropy Based on Belief Functions

Table 5

Out-of-sample forecasting performance.

	TRUE
Forecast 2014	0.009	0.0357	0.0367	0.0331	0.0367	0.0042	0.0039	0.0030
prediction range		[0.0123, 0.0838] 0.0715	[−0.0191, 0.0918] 0.1109	[−0.0157, 0.1072] 0.1229	[−0.0054, 0.1172] 0.1226	[−0.0226, 0.0381] 0.0607	[−0.0225, 0.0387] 0.0613	[−0.0218, 0.0383] 0.0601
Forecast 2015	0.030	0.0331	0.0328	0.0338	0.0348	0.0404	0.0419	0.0410
prediction range		[−0.0150, 0.0812] 0.0962	[−0.0187, 0.0882] 0.1069	[−0.0153, 0.1006] 0.1159	[0.0016, 0.1035] 0.1019	[−0.0496, 0.1305] 0.1801	[−0.0493, 0.1351] 0.1844	[−0.0490, 0.1309] 0.1799
Forecast 2016	0.033	0.0340	0.0352	0.0338	0.0362	0.0398	0.0401	0.0407
prediction range		[−0.0128, 0.0808] 0.0936	[−0.0162, 0.0887] 0.1049	[−0.0133, 0.0976] 0.1109	[0.0001, 0.1107] 0.1106	[−0.0467, 0.1252] 0.1719	[−0.0433, 0.1212] 0.1645	[−0.0439, 0.1231] 0.1670
Forecast 2017	0.039	0.0341	0.0344	0.0339	0.0353	0.0395	0.0385	0.0386
prediction range		[−0.0115, 0.0798] 0.0913	[−0.0162, 0.0838] 0.1000	[−0.0116, 0.0950] 0.1066	[0.0006, 0.1058] 0.1052	[−0.0439, 0.1214] 0.1653	[−0.0431, 0.1225] 0.1656	[−0.0425, 0.1207] 0.1632
Forecast 2018	0.041	0.0340	0.0334	0.0344	0.0357	0.0395	0.0390	0.0405
prediction range		[−0.0099, 0.0793] 0.0892	[−0.0151, 0.0810] 0.0961	[−0.0099, 0.0941] 0.1040	[0.0019, 0.0983] 0.0964	[−0.0414, 0.1185] 0.1599	[−0.0423, 0.1191] 0.1614	[−0.0431, 0.1206] 0.1637
MAE		0.0038	0.0043	0.0034	0.0053	0.0023	0.0023	0.0024
RMSE		0.0126	0.0129	0.0153	0.0130	0.0059	0.0066	0.0066
Mean of prediction range		0.0884	0.1038	0.1119	0.1073	0.1476	0.1475	0.1467

norm = normal likelihood, std = student-t likelihood, sstd = skewed student-t likelihood, and is the point prediction.