The combination forecasts of OP reduce MSFE
relative to the AR benchmark by 25% on average.
Under the null hypothesis, the two models have equal MSFE
, while under the alternative the MSFE
of the alternative model is less than that of the benchmark.
Note: Numbers are the MSFE
; p-values of the MCS are reported in parentheses; * denotes that the model belongs to the 5% of the MCS of Hansen et al.
At the horizon of one year, only the linear and quadratic trend models produce slightly lower MSFE
than the random walk forecast while all other models have larger MSFE
than the random walk forecast.
Under the null hypothesis of equal forecasting ability, [MSFE.sub.0] = MSFE
, so that d and MSE-T are equal to zero.
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.
= [1/M] [M.summation over (i=1)] ([[sigma].sup.2.sub.i]] - [[??].sup.2.sub.i]])[sup.2] (26)
First, including the CFNAI in our forecasting regressions on NIPA data results in a substantial improvement in forecast accuracy (MSFE
ratios less than 1) for GDP and measures of business investment, particularly at shorter horizons.
The final-period impulse indicator essentially takes the forecast back to a random walk, with MSFE
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.
Recursive Neural OLS Network SPF SPF (Current Quarter) (1) (2) (3) (4) MFE 0.001 0.004 0.09 -0.04 MAFE 0.10 0.09 0.21 0.11 MSFE
0.0156 0.0138 0.073 0.0169 RMSFE 0.125 0.117 0.27 0.13 Theil's U 0.57 0.54 1.12 0.55 P-val.
To investigate this assumption, we compare the mean squared forecast error (MSFE
) across the sophisticated and unsophisticated subsamples.