Roland Dohrn
α2 =0, which can be tested by a simple t-test. Holden/Peel (1990) suggest the
null hypothesisα0=0,α1=1andα2 =0 and to apply an F-test instead.
2.2 A Non-parametric Test
However, these tests might be inappropriate in the case at hand for various
reasons. First of all, the number of observations is rather small here, so that the
results of the test may be spurious. This problem is aggravated by the fact that
in short term forecasts the total error typically can be attributed to a rather
small number of cases in which forecast errors are extraordinary large.
Therefore it may be more appropriate to employ non-parametric tests as e.g. a
sign test which has been suggested for similar applications (e.g. forecast com-
parisons; Diebold, Mariano 1999: 392). A less sophisticated testing technique
may also be suitable because of the quality of the data: On the one hand, real
time data for the indicators x would be required to get a adequate picture of
the forecaster’s information background. These are, however, hard to collect
for many indicators. On the other hand, the forecast errors measured can only
be approximations of the “true” error, because many institutions rounded off
their forecast values to 0.5 percentage points until the late 1990s.
Therefore the subsequent analyses will be based on a non-parametric test
which has been proposed by Campbell/Ghysels (1995). In the following the
forecast errors will be denoted as
(4)
et=ft-rt.
As the test is based on the number of positive signs of e,it can only be applied
for unbiased forecasts. Therefore, a sign test for unbiasedness will be applied
at first whether the median forecast is 0
(5)
where:
S=∑I+(et)
t
[ 1 if et > 0
I (e. ) = i t
+(et ) |0 otherwise.
S is cumulative binominal distributed with probability 0.5. In our case (n = 14),
unbiasedness must be rejected in a two tailed test on a 10% level, if the
number of positive signs is not larger than 3 or above 11 (5%: 2 or 12; 1%: 1 or
13). To take into account a potential bias, et will be corrected subsequently by
subtracting the median bias
(6)
etc =et-median(et-n,et-n+1,...,et).
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