Table 6.
Mode1 1 |
Model 2 |
|||
---|---|---|---|---|
h = 10 | h = 20 | h = 10 | h = 20 | |
RMSE | 0.2954 | 0.2758 | 0.7253 | 0.6966 |
MAD | 0.4685 | 0.4532 | 0.5247 | 0.5031 |
MAPE | 728.076 | 678.195 | 2034.644 | 1950.854 |
Clark & West | – | 0.2140*** (0.0646) [3.3118] |
– | 0.1928*** (0.0583) [3.3046] |
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.