Table 13.

Univariate and multivariate selected models and error out-sample

Data	OUT	OUT-ALL				OUT-MEAN
		Univariate		Multivariate		Univariate		Multivariate
	Regions	Model	RMSE	Model	RMSE	Model	RMSE	Model	RMSE
RJ	R 1	NNETAR	16.5	SSM-M	93.3	NNETAR	13.2	SSM-M	20
	R 2	ARIMA	51.5	VAR	90.9	ES	43.5	VAR	56.9
	R 3	MLP	92.5	VAR	92.2	ES	65.8	VAR	86
	R 4	MLP	34.3	SSM-M	84.1	ES	33.9	VAR	42.2
	R 5	MLP	91.7	VAR	92.1	TBATS	54.9	VAR	69.6
Italy	CEN	TBATS	364.9	SSM-M	2104.3	TBATS	355.3	SSM-M	589.7
	ISL	ES	454.3	VAR	1496.7	ES	143.4	SSM-M	262.5
	NOW	TBATS	542.1	SSM-M	1843.5	TBATS	498.3	SSM-M	833.9
	NOE	TBATS	674.7	SSM-M	2049.1	ES	673.7	SSM-M	1231.9
	SOT	TBATS	488.4	SSM-M	1860.5	ES	368.7	SSM-M	565.0
US	AZ	TBATS	617.7	VAR	1986	ES	557.2	VAR	900
	CA	ARIMA	6838	SSM-M	5643.6	ARIMA	1959.1	SSM-M	785.1
	NV	NNETAR	246.7	VAR	406.5	MLP	157.2	VAR	298.1
	OR	SSM-U	268.6	VAR	117.4	ARIMA	148.9	SSM-M	115.7

Source: The authors