Table 8.

RI results: SARIMA-MIDAS₃ vs. other benchmark models.

Models	SNAÏVE	ETS	SARIMA	SARIMAX1	SARIMAX2	SARIMAX3	SARIMAX4	SARIMA-MIDAS1	SARIMA-MIDAS2
1-step-ahead forecasting
MAPE	0.8208	0.7300	0.6546	0.6062	0.6234	0.5944	0.5521	0.3007	0.1391
RMSPE	0.8099	0.7523	0.6603	0.6446	0.6593	0.6224	0.5865	0.3942	0.2950
RMSE	0.9387	0.8921	0.6381	0.6916	0.6384	0.6069	0.5837	0.3934	0.2628
MAE	0.9199	0.8815	0.6450	0.6352	0.6141	0.5873	0.5509	0.2988	0.1137
2-steps-ahead forecasting
MAPE	0.8297	0.7813	0.6735	0.6581	0.6128	0.6473	0.5316	0.3760	0.1903
RMSPE	0.7944	0.7522	0.6430	0.6283	0.6305	0.6185	0.5500	0.4023	0.1768
RMSE	0.9262	0.8767	0.6520	0.5858	0.6472	0.5712	0.5671	0.3956	0.1881
MAE	0.9188	0.8975	0.6749	0.6359	0.6223	0.6221	0.5398	0.3694	0.1938
3-steps-ahead forecasting
MAPE	0.7965	0.7455	0.6641	0.6170	0.6151	0.5639	0.4849	0.3142	0.1245
RMSPE	0.7776	0.7023	0.6560	0.6088	0.6061	0.6179	0.5057	0.3775	0.1333
RMSE	0.9312	−0.0820	0.6409	0.6051	0.6018	0.6854	0.5356	0.4072	0.1353
MAE	0.9109	0.0543	0.6574	0.6165	0.6144	0.6092	0.5006	0.3341	0.1268
4-steps-ahead forecasting
MAPE	0.7957	0.7479	0.6549	0.6579	0.6391	0.6138	0.6007	0.3540	0.0909
RMSPE	0.7554	0.7297	0.6222	0.6236	0.5927	0.6120	0.5684	0.3499	0.0435
RMSE	0.9121	0.8675	0.6292	0.5853	0.5134	0.5463	0.5331	0.2849	0.0215
MAE	0.9019	0.8823	0.6540	0.6339	0.6000	0.5780	0.5777	0.3130	0.0614
5-steps-ahead forecasting
MAPE	0.7625	0.7149	0.6446	0.6327	0.6273	0.6122	0.6300	0.3758	0.2108
RMSPE	0.7029	0.6762	0.6052	0.5822	0.5787	0.5577	0.5873	0.3796	0.2338
RMSE	0.9101	0.8747	0.6755	0.6537	0.6525	0.6160	0.5789	0.4354	0.2469
MAE	0.8970	0.8834	0.6806	0.6681	0.6637	0.6372	0.6214	0.4034	0.2055
6-steps-ahead forecasting
MAPE	0.7531	0.6990	0.7474	0.7167	0.7029	0.6128	0.6197	0.4200	0.1944
RMSPE	0.7235	0.7084	0.7360	0.7021	0.6861	0.6388	0.6369	0.4125	0.1871
RMSE	0.9131	0.8739	0.7212	0.6837	0.6665	0.6943	0.6729	0.3803	0.1646
MAE	0.8919	0.8702	0.7388	0.7065	0.6930	0.6511	0.6424	0.4038	0.1973