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. 2021 Jan 12;74:101666. doi: 10.1016/j.irfa.2021.101666

Table 6.

Out-of-Sample Forecast evaluation [Pre-COVID Announcement].

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.