## Version: 2000 Feb. 20

How well can nowcasting serve as a forecasting tool? Clearly enough, if
nowcasting indicates a *propensity*, then it can be used actively to
ensure that a desired situation will come about. In the following, we will
look at the extent to which a nowcast is related to what happens afterwards.
We run the nowcast along the time series, taking each point (from time
point 1000 onwards) and carrying out a nowcast at up to 11 resolution
scales. We are using a set of 6160 futures values.
The original data can be seen in Figures 2 onwards. The following
figure shows the wavelet transform.

To show the procedure followed, consider the result at scale 10. We
will look at the significant upward or downward "signals".

Scale 10 is found to contain six significant upward or downward transitions.
The figure above shows their locations. From left to right, they are

downward,

upward,

downward,

upward,

downward, and

upward.

There is a
relatively good relationship between these indicators of subsequent
performance.

Let us have a look at the cumululative effect of these up and down
signals. We will code these as +1 and -1 (unweighted). Furthermore,
we will simplify the analysis by taking all scales into account without
any weighting for the different scales. For scales 1 to 11, we find the
numbers of significant up and down "signals" to be (respectively):
206, 1000, 632, 347, 162, 73, 46, 25, 12, 6, 1. The following figure
shows a plot of the input data, and a plot of the cumulative up/down
nowcasts. The number of up/down signals considered is 206 + 1000 + ...
+ 1 = 2510. We recall that the number of values in the input data set
is 6160, and that the nowcasts were carried out from time point 1000 onwards
implying that the 2510 significant up/down signals were extracted from a
total of 5161 nowcast values.

We recall also that
this is simplified version of our results in that we are taking all
up and down signals as equally important (+1 and -1), and furthermore all
scales as equally important.

To test the tracking, and therefore genuine forecast, ability of the
signficant nowcasts, with reference to the previous figure, we will look
at how the significant up/down signals are related to the one-step ahead
upward and downward movements in the original time series. The
unweighted movement
up or down will be used (coded +1 or -1).

Significant nowcast __up__, 1-step ahead original data __up__:
__700__

Significant nowcast __down__, 1-step ahead original data __down__:
__716__

Significant nowcast __up__, 1-step ahead original data __down__:
__269__

Significant nowcast __down__, 1-step ahead original data __up__:
__240__

Cases 1 and 2 here lead to a correct tracking result of 73.5%. We had
significant nowcasts in 48.6% of all possible time-points.

If we consider cases 1, 2 and 4 above as being desirable, then the correct
tracking result is 86.0%.

**Acknowledgement**

Data from Mark Savage.