From forex forecast to forex signal. Level 0 forecast discrimination.

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Written by Forex Automaton   
Wednesday, 20 January 2010 17:53

Some opportunities for analysis are offered by the fact that the forex trading system such as Danica gives not just a forecast for the next close, but a combination of next high, low and close. This report is the first attempt to develop a selective approach to the forecasts, a discrimination algorithm of sorts, such that a decision to give the forecast further consideration or ignore it would be based on the information contained in the forecast itself.

Ultimately the (currently) missing link between the forecast and a decision to trade may well take the shape of a cascade of selection decisions, each rejecting a certain fraction of forecasts, leading to a purer sample of actionable ones, enriched in terms of the reward to risk ratio. The number of such purifying rejection steps is of course limited by the depth of information within the forecast and the available real-time data about the conditions of the markets. One obvious step is to look at the relationship between the forecast directions of day-to-day change in the day's high, low and close. These can be classified in the way summarized in the following table:

 

high & close direction

opposite

same

low & close direction

opposite

0 (5.6)

1 (6.7)

same

2 (7.3) 3 (80.4)

Table 1. Definition of trigger words (0,1,2,3) used in the study. Their prevalence in % is shown in parentheses. The background colors of the fields correspond to those of the data in Fig.1, for the respective data.

The term trigger word will be used to denote a unique combination of bits used to classify a situation (an event of a forecast) according to pre-selected criteria. Situations or events having similarity within the chosen analysis framework are assigned the same trigger word. In Table 1, forecasts are classified according to the similarity or dissimilarity of the forecast sign of change (up or down) among the three quantities being forecast.  Trigger word "3" denotes events with the highest consistency of forecasts (either all three up or all three down).

Pearson correlation of predicted and  actual day-scale forex logarithmic returns (high) as a function of  the forecasting parameter. 1.1 Pearson correlation of predicted and  actual day-scale forex logarithmic returns (low) as a function of  the forecasting parameter. 1.2 Pearson correlation of predicted and  actual day-scale forex logarithmic returns (close) as a function of  the forecasting parameter. 1.3

Fig.1. Pearson correlation of predicted and actual day-scale logarithmic returns in high (1.1), low (1.2) and close (1.3) as a function of the forecasting parameter nicknamed Fred. The shaded bands indicate a measure of uncertainty, their boundaries mark one standard deviation (among the forex pairs considered) distance to the points. Back-testing simulations give the forecasing engine no access to the future data, direct or indirect. Significantly positive (and ideally, large) values correspond to quality forecasting. Note that the quantities at different Fred are not quite statistically independent, therefore the error bands should be understood as describing the uncertainty of the position of the curve at large rather than that of individual points.

Fig.1 demonstrates that such a trigger word selection has a very visible effect on the forecasting quality for high and low: the large separation among the colored curves in panels 1.1 and 1.2 is undeniable. A very interesting symmetry is seen between 1.1 and 1.2: while the data sets labeled as "0" and "3" look similar, "1" and "2" seem to swap places as we go from high (1.1) to low (1.2).

The worst overall situation for the predictability of day's high (1.1) is the one when high and close are forecast to move in the opposite directions (trigger word "2"). Panel 1.3 indicates that, surprisingly, forecast quality for close does not look compromised at all in the same situation. In other words, while forecast quality for high is, on average, considerably better than it is for close, it is the former that should not be trusted in case of a discrepancy.

The situation with predictability of day's low is, modulo the uncertainty marked by the shaded bands, a mirror reflection of that with the high: the quality of day's low forecast suffers when low and close are forecast to move in the opposite directions (trigger word "1").

Fig.1 reinforces the view that day close (panel 1.3) is the hardest one to forecast. Large scatter of the points does not allow one to draw a definite conclusion regarding the impact of the individual trigger words. Therefore from panel 1.3, there is no separate argument in favor or against trigger "3" as the one to be preferred; however evidence from panels 1.1 and 1.2 looks suffucient to prefer "3" and reject (veto) the other three types. This would be a fairly mild discriminator as only about 20% of forecast events would be vetoed. Note that the decision making does not involve much math: trigger "3" would consist in making sure all three predicted day-to-day differences in high, low and close have the same sign: a decision which is easy to make on the basis of Danica's text output.

Finally, the shapes of the Fred dependence seen previously would not be much changed by the decision to use trigger "3" only: the quantity 28 used in Danica since version 0.5 still looks like a good choice.

This study is based on data from 2002-08-20 through 2010-01-15, with the trading day defined to begin and end 9am Eastern time.

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Last Updated ( Friday, 21 May 2010 09:56 )