Dynamic spatiotemporal correlation coefficient based on adaptive weight

Financial Innovation

Table 6 VaR forecasting results based on the two correlations (Christoffersen test (Christoffersen, 1998))

Back-testing	Confidence level	VaR forecasting with time series correlation	VaR forecasting with spatio-temporal correlation	Back-testing	Confidence level	VaR forecasting with time series correlation	VaR forecasting with spatio-temporal correlation
Stage 1				Stage3
UC	0.95	0.3055	21.6723	UC	0.95	61.7318	17.7670
UC	0.95	(0.5805)	(0.0000)	UC	0.95	(0.0000)	(0.0000)
IND	0.95	2.7388	0.024	IND	0.95	9.9949	6.0112
IND	0.95	(0.0979)	(0.8768)	IND	0.95	(0.0016)	(0.0142)
CC	0.95	3.0443	21.6963	CC	0.95	71.7267	23.7782
CC	0.95	(0.2182)	(0.0000)	CC	0.95	(0.0000)	(0.0000)
Stage 2				Stage 4
UC	0.95	0.0918	85.3128	UC	0.95	11.4028	0.0069
UC	0.95	(0.7619)	(0.0000)	UC	0.95	(0.0007)	(0.9336)
IND	0.95	5.4974	0.0080	IND	0.95	0.4184	4.8701
IND	0.95	(0.019)	(0.9286)	IND	0.95	(0.5177)	(0.0273)
CC	0.95	5.5892	85.3208	CC	0.95	11.8212	4.8770
CC	0.95	(0.0611)	(0.0000)	CC	0.95	(0.0027)	(0.0873)

The table presents significance p values and their corresponding statistics in the VaR backtesting examination. Where, the statistical values are outside the brackets, and the p values are inside the brackets. The lower statistics (higher p-values) in the UC, IND, and CC tests, the better results are. According to Kupiec (1995) and Candelon et al. (2011), the forecasting results cannot be rejected if significance of p values are bigger than 0.05