Table 9.

12-step-ahead forecast comparisons 2001:3–2005:1.

Model $j$	$H_0:{\text{MSE}}_i={\text{MSE}}_j\text{ vs }{H}_a:{\text{MSE}}_i<{\text{MSE}}_j$				MSE	MAPE
	Model $i$
	HTM	LVARX	DLVARX	ARIMA
US visitors
HTM		1.000	0.966	0.033	0.0356	0.0212
LVARX	0.000				0.0566	0.0331
DLVARX	0.034				0.0433	0.0278
ARIMA(3, 1, 2)	0.967				0.0231	0.0212
JP visitors
HTM		1.000	1.000	1.000	0.0266	0.0272
LVARX	0.000				0.0551	0.0395
DLVARX	0.000				0.1356	0.0454
ARIMA(0, 1, 1)	0.000				0.1140	0.0568
Room price
HTM		0.455	0.038	1.000	0.0032	0.0089
LVARX	0.545				0.0031	0.0108
DLVARX	0.962				0.00122	0.0050
ARIMA(0, 1, 0)	0.000				0.0188	0.0272
Occupancy
HTM		1.000	1.000	0.0000	0.0022	0.0570
LVARX	0.000				0.0085	0.1160
DLVARX	0.000				0.0111	0.1218
ARIMA(2, 1, 3)	1.000				0.0009	0.0357

Note: Each panel presents results for a different target variable. In each case, column 1 lists competitor model $j$, and columns 6–7 present the Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE) for the model $j$ forecasts. Columns 2–5 list competitor models $i$ and present the $p$-values for a test of the null hypothesis that $H_0:{\text{MSE}}_i={\text{MSE}}_j$ versus the alternative hypothesis, $H_a:{\text{MSE}}_i<{\text{MSE}}_j$. Thus, $p$-values below the conventional 5% significance level in column 2 indicate a rejection of the hypothesis that the MSE of the HTM forecast is equal to its competitor forecast from model $j$ in favor of the alternative that the HTM forecast produces a smaller MSE. For each forecast target, the minimum MSE and MAPE are underlined, as are $p$-values below the conventional 5% significance level.