Forecasting Using Information and Entropy Based on Belief Functions

Table 3

Forecasting performance.

	Normal likelihood-based belief function	Student-t likelihood-based belief function	Skewed Student-t likelihood-based belief function	Shannon entropy-based belief function	Renyi entropy-based belief function	Tsallis entropy-based belief function
	T = 20
	0.9346 (0.9541)	1.2327 (1.8079)	13.8763 (15.4710)	0.5784 (0.5824)	0.5796 (0.5831)	0.5788 (0.5826)
	T = 40
	0.6891 (0.7552)	1.6996 (1.6252)	8.7598 (12.2013)	0.2596 (0.5914)	0.2608 (0.5948)	0.2605 (0.5953)
	T = 20
	0.4601 (0.5491)	1.2275 (1.4574)	2.0607 (2.4733)	0.5582 (0.7576)	0.5688 (0.7589)	0.5591 (0.7601)
	T = 40
	0.4995 (0.3136)	1.4068 (1.4647)	1.2092 (1.1063)	0.5294 (0.3787)	0.5301 (0.3793)	0.5312 (0.3798)
	T = 20
	1.2850 (1.476)	1.1815 (2.6127)	1.6660 (1.8974)	1.2191 (1.7849)	1.2115 (1.7858)	1.2114 (1.7857)
	T = 40
	0.7604 (0.4309)	0.6142 (0.3654)	0.8783 (1.1256)	0.7538 (0.2542)	0.7542 (0.2550)	0.7542 (0.2550)
	T = 20
	0.7278 (0.9846)	2.6995 (2.0442)	0.5878 (1.1307)	0.6699 (1.6189)	0.6703 (1.6208)	0.6700 (1.6200)
	T = 40
	0.5520 (0.4491)	1.4772 (1.2513)	0.4443 (0.8051)	0.4513 (0.3370)	0.4559 (0.3389)	0.4564 (0.3401)

() is standard deviation on . The bold numbers present the best prediction result.