The forecasting performance of the models is assessed by calculating the ratio of the MSFE
of each model over the MSFE
of the benchmark (Eq.
We test this null hypothesis against the one-sided (upper-tail) alternative hypothesis that the MSFE
for the unrestricted model forecasts is less than the MSFE
for the restricted model forecasts ([MSFE
Columns 2 and 6 represent the root MSFE
(RMSFE) of the linear AR model for both the real, rand-dollar and rand-pound exchange rates, hereon referred to as the United States and United Kingdom respectively.
TABLE 1 Pseudo out-of-sample relative MSFE
ratios FCI Adjusted Adjusted h CFNAI residual FCI FCI residual A.
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.
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).
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.
Thus, scaling the MSFE
by either book value or market price does not appear to alter the results.
is the mean-squared forecast error, and RMSFE is the square root of the mean squared forecast error.
Table 3 indicates that the DS forecasts at 1-step ahead are often significantly more accurate than those of the TS model on MSFE