Selecting Single Model in Combination Forecasting Based on Cointegration Test and Encompassing Test

Table 4

Unit root test on fitting data of 12 single forecasts.

Test sample	ADF statistics	1% critical value	IS stable	ADF statistics after first difference	1% critical value	IS stable after first difference	Result
Forecast sample	2.66	−3.59	No	−5.03	−3.60	Yes	𝐼(1)
Naive	−6.02	−3.60	Yes	—	—	—	𝐼(0)
SINGLE	−6.02	−3.60	Yes	—	—	—	𝐼(0)
Holts	1.65	−3.60	No	−7.53	−3.59	Yes	𝐼(1)
DAMPEN	0.15	−3.60	No	−16.02	−3.61	Yes	𝐼(1)
WINTE	4.20	−3.59	No	−15.31	−3.61	Yes	𝐼(1)
THETA	5.12	−3.59	No	−9.01	−3.60	Yes	𝐼(1)
ARIMA	3.31	−3.60	No	−7.59	−3.59	Yes	𝐼(1)
ARARMA	2.08	−3.60	No	−11.4	−3.60	Yes	𝐼(1)
Auto-ANN	10.8	−3.61	No	1.55	−3.59	No	𝐼(2) or more
NARX	5.21	−3.60	No	−19.74	−3.60	Yes	𝐼(1)
GM(1, 1)	3.11	−3.59	No	−12.56	−3.59	Yes	𝐼(1)
SVM	4.10	−3.60	No	−4.21	−3.60	Yes	𝐼(1)