Roland Dohrn
Gaussian distribution can be applied after having standardized WO2. In the
present case, the critical values calculated from the Gaussian distribution
differ little from those taken from the tables. As the application of the
Gaussian distribution makes it easier to conduct a large number of tests, it will
be applied here.
2.3 Type I and Type II Errors
When using data to make a prediction, forecasters may be wrong in two ways.
Firstly, they may neglect some indicators that would be useful for the forecast,
or they underestimate their influence (type I error). Secondly, they may put
too much emphasis on an indicator (type II error). These two cases will be il-
lustrated by an example: If business surveys indicate more optimistic expec-
tations in the manufacturing sector (xtc is positive), some forecasters may
revise their prediction on GDP upward, some not. After GDP figures being
published, and having compared forecasts with realisation it may turn out, that
some forecasters may have been too pessimistic, because they did not suffi-
ciently pay attention to the business expectation index. In the terminology
used here, they made a type I error. If this happened several times in the past,
forecast errors tend to be negative whenever business expectations improved.
Hence, a type I error would show up in low values of WO. Some forecasters, on
the other hand, may overdue. They may take any indication that expectations
improve to revise their forecast upward, what in the rear view may turn out to
be over-optimistic. That is the typical case of the type II error. It will lead to
high values of WO. To be able to distinguish these two cases, all x c variables in
this study will be standardized in a way that positive (negative) values van be
interpreted as indicators of high (low) growth rates.
3. Data Description
3.1 Forecasts Analysed
Subsequently the information efficiency of the forecasts produced by RWI
Essen and the Gemeinschaftsdiagnose (GD) will be tested. Both predictions
are outcomes of a national accounts based iterative forecasting procedure,
which allows integrating various forecasting techniques. Hence it is not clear,
what role the indicators considered later play in the end in making these
forecasts. Therefore, this kind of forecast is highly suitable for the analyses
carried out here.
2
2 The mean of the Wilcoxon test statistic with n observations is (n + 1)/4and its variance
n(n+1)(2n+1)/24. In the literature different thresholds can be found to mark whether a sample
is large.