Table 1.

Ljung-Box Q test of the residuals for each of the selected optimal models.

Lags	Residuals of ARIMA model		Residuals of ETS model		Residuals of hybrid model
	Ljung-Box Q	P	Ljung-Box Q	P	Ljung-Box Q	P
1	0.002	0.969	0.000	0.990	0.807	0.369
3	0.225	0.973	0.339	0.953	3.671	0.299
6	2.800	0.833	13.479	0.036	7.022	0.319
9	5.141	0.822	18.900	0.026	9.690	0.376
12	12.180	0.431	33.050	0.001	11.413	0.494
15	14.892	0.459	37.469	0.001	12.601	0.633
18	16.199	0.579	42.457	0.001	15.396	0.635
21	17.127	0.703	44.570	0.002	19.761	0.536
24	18.414	0.782	47.079	0.003	20.694	0.657
27	19.932	0.834	49.803	0.005	24.873	0.582
30	23.542	0.792	53.888	0.005	30.349	0.448
33	29.190	0.657	58.505	0.004	32.664	0.484
36	29.713	0.761	58.715	0.010	35.564	0.489