These rankings suggest that the forecast encompassing statistics, especially ENC-NEW, can have important power advantages over test statistics based on relative MSFE.
When we move to the relative MSFE metric, we find that barring few cases (six-months, nine-months and twelve-months ahead forecast horizons for M1 and one-month ahead forecast horizon for the first-differenced lending rate), the value of the Theil's U is less than one for all the cases where we found in-sample predictability.
so will yield a lower MSFE
when [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], which is a standardised location shift greater than one error standard deviation, independently of [[lambda].
Owing to the assumption of heteroscedasticity, standard errors and significance are not presented; however, using a homoscedastic fixed regressor bootstrap, we can reject the null of equal MSFE for nearly all months.
A homoscedastic bootstrap (which as mentioned can produce an approximation for inference testing) also rejects the null of equal MSFE for Germany and for several months for Canada, France, and Japan.
This is true despite the fact, that the ARDL model MSFE almost always exceeds the AR benchmark model MSFE (as in Stock and Watson 2003).
As indicated above, they find that out-of-sample forecasts for the 1985:1-1999:4 period generated by ARDL models that include financial variables typically have an MSFE that is substantially larger than the MSFE from an AR benchmark model.
If the relative MSFE of the candidate forecast is less than one, then the forecast based on that leading indicator outperformed the AR benchmark in the period just before and during the 2001 recession.
In principle, it would be desirable to report a standard error for the relative MSFE in addition to the relative MSFE itself.
MSFE is the mean-squared forecast error, and RMSFE is the square root of the mean squared forecast error.
The test results shown in Table 4 reject the null of equal MSFE for [F.
Table 3 indicates that the DS forecasts at 1-step ahead are often significantly more accurate than those of the TS model on MSFE