## 451: Forecast Series

Tables of the forecasts for individual gridpoints/stations/series and a graph of the historical and current forecast(s) are shown. The table shows the years for which the forecasts apply, some information about the definitions of the categories, and the forecasts themselves, presented in different formats.

In the thresholds box (top left) the climatological period is first indicated, and defines the data used to define the categories. The thresholds dividing the categories are then given in the units of the original data, possibly standardised depending on the standardisation option. For example, if the original data are in mm, and the anomaly standardisation is selected, the thresholds will be in mm anomalies from the climatological average. The climatological probabilities, below, show the proportion of years in the climatological period that were in each category. By default these probabilities will be 33% (assuming there are no ties, in which case the probabilities may deviate from 33% somewhat), but the actual probabilities will depend upon the threshold settings. The climatological odds are equal to the probability that the category in question was observed, divided by the probability that it was not observed. For example, if the climatological probability of "above-normal" is 33% the odds will be 0.5 ("above-normal" occurs half as often as "normal" and "below-normal" combined, i.e., it occurs half as of often as it does not occur).

The forecasts box presents the forecast in different formats. Probabilistic forecasts and odds are presented first. If the
climatological probabilities are equiprobable and the forecast probability for the "normal" category is the lower than for the
outer categories, it may be worth
transforming
the Y data so that they are normally
disrtibuted. Applying the transformation will require CPT to
reset
. The probabilities are
derived from the best-guess forecast (listed as "Forecast" under "Forecast ranges") by assuming that the errors in the
best-guess forecast will be normally distributed (or, more strictly, follow a Student's
*
t
*
distribution), with the
variance of the errors defined by the variance of the errors in the cross-validated predictions (alternative error variances
can be set using
Options ~ Forecast Settings
). If the Y data have been
transformed
it is assumed that the forecast errors of the transformed data will be
normally distributed. From the best-guess forecast and the assumed error variance and distribution the probabilities of
exceeding the various thresholds can be calculated. Prediction intervals can also be calculated for a given level of
confidence. The prediction intervals are shown as the upper and lower limits under "Forecast ranges". The default is to define
the intervals as one standard error from the best guess, which translates to a confidence level of about 68%. The default can
be adjusted using
Options ~ Forecast Settings
.

The graph shows the history of the cross-validated forecasts (green line) and observations (red line), and the current forecast(s) shown by green crosses. The prediction intervals for the forecasts can be added by right-clicking on the graph, and following the "Customise" option. The vertical coloured divisions show the three categories. Note that when calculating the cross-validated forecasts, the threshold defintions will have fluctuated slightly, and so the current categorisation fo the forecasts and observations may not exactly match the cross-validated classification. This fluctuation is the reason for any apparent discrepancies between the graph and the contingency tables .

The forecasts can be saved by selecting the
**
Forecasts
**
tab from the
File _Output
Results
) menu. The graph itself can be exported as a graphics file by right-clicking anywhere in the child window and
selecting
Export
from the pop-up menu. A default name is given to the graphics file, but this name
can be changed using the browse button. The image quality for all the graphics formats can be improved by increasing the size
of the image (see
Options ~ Graphics ~ Graph Scaling
). The graphic title can be
set using the
**
Customise
**
option upon right-clicking in the child window.

The y-axis limits can be set by right-clicking on the image and then selecting the
**
Customise ~ Y-Axis Limits
**
option. The
maximum and minimum values on the y-axis are indicated and can be reset. Resetting these axis limits will in turn automatically
reset the tick-mark interval and number of tick marks. Greater flexibility for setting the tick marks is planned for future
releases. Further options for customising the graph, including adjusting the size of the fonts, and the size of the images, are
available from
Options ~ Graphics
.