Table 7.
Mode1 1 |
Model 2 |
|||
---|---|---|---|---|
h = 10 | h = 20 | h = 10 | h = 20 | |
RMSE | 1.2006 | 1.1299 | 1.4706 | 1.4092 |
MAD | 0.9928 | 0.9720 | 0.9717 | 0.9273 |
MAPE | 1186.005 | 1073.689 | 759.618 | 724.923 |
Clark & West | – | 0.9954*** (0.4697) [2.1193] |
– | 0.8782*** (0.4227) [2.0779] |
Note: Model 1 incorporates the Uncertainty (VIX) predictor while Model 2 is the Historical Average. Thus, the former is the unrestricted model while the latter is the restricted model. RMSE is Root Mean Square Error; MAD is Mean Absolute Deviation & MAPE is Mean Absolute Percentage Error. The results for the Clark & West are reported for the model under the null (i.e. Model 2). The RMSE reported for Model 1 is the version of Clark and West (2007) which adjusts the difference in mean squared prediction errors to account for the additional predictors in the model. *** and ** & * imply the rejection of the null hypothesis of equal forecast accuracy at 1%, 5% & 10% levels of significance, respectively. The null hypothesis of a zero coefficient is rejected if this statistic is greater than +1.282 (for a one sided 0.10 test), +1.645 (for a one sided 0.05 test) and + 2.00 for 0.01 test (for a one sided 0.01 test) (see Clark & West, 2007). Two out-of-Sample forecast horizons are considered: 10-day & 20-day ahead forecast horizons. Values in parentheses - () denote standard errors while those reported in square brackets – [] are for t-statistics.