Prediction quality for high, low is improved by tying the four components of a day candle together.

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Written by Forex Automaton   
Friday, 18 December 2009 11:57

In this week' update, I demonstrate an improvement in the prediction quality for day low and high in six major forex pairs -- EUR/USD, USD/JPY, GBP/USD, USD/CHF, AUD/USD, and USD/CAD -- by imposing the obvious constraints of low being below high and day's open (which is assumed in forex to coincide with previous day's close) being between the day's low and high. As before, I use Pearson correlation coefficient between the real and predicted logarithmic returns, as a figure of merit to gauge the prediction quality. Contrary to my expectation, no visible improvement for close is obtained by such technique. The results have to be compared with the previous report.

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

Fig.1. Pearson correlation of predicted and actual day-scale logarithmic returns in low, high and close 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.

Day scale data for EUR/USD, USD/JPY, GBP/USD, USD/CHF, AUD/USD, USD/CAD covering the time span from August 20, 2002 through August 21, 2009 are used in Fig.1. The middle and half-width of the bands around the data points in Fig.1 represent the mean and standard deviation of the set of the individual Pearson correlation coefficients for the 6 major forex exchange rates, treated as independent measurements.

Any time point in the analysis is represented by a triplet of price-related quantities: the logarithmic returns of high, low, and close. Due to 24-hour nature of forex, the open is typically so tightly related to the previous close that it makes little sense to consider the next open -- previous close pair as independent variables, and an either one can be chosen. There is a certain lack of statistical independence in the logarithmic returns among the low, high and close: there is a constraint that next low be below next high and the close be between them. Therefore strictly speaking there is a certain amount of "trivial" redundancy built in. The triplets are analyzed jointly (in the same sense as different markets are analyzed jointly in the Step three algorithm). One way of taking advantage of the high and low predictions is to require that the natural relationship (low below close, close below high) holds. This has not been done in the past, but is implemented in the version of the system under study.

This is done in two steps:

  1. If the predicted low (high) is above (below) tomorrow's open which is, due to the continuous nature of forex trading, assumed to be identical to today's close, then the predicted low (high) is moved down (up) to match tomorrow's open.

  2. After that, we are left with the task of adjusting predicted low, high and close in a similar way. The difference is that unlike next open, it seems unjustified to assign a lot of significance to the next close. In the present version of the algorithm, if predicted close is outside the low-high interval, both close and high (low) are changed so that the adjusted close and high (or low -- depending on the direction of the deviation of predicted close) are replaced both with the same value wich is half-way between them. Effectively, the two are given equal weight.

As a result of the second step (if the second step takes place at all), the results of the first one are not invalidated, since the second step can only broaden the low-high interval.

The steps were implemented one after another, checking the results. Fig.1 shows the result of both steps. It is interesting that while the first step had the effect of improving the figure of merit in Fig.1 (the correlation coefficient increased from 0.3 at most in the previous report to 0.39 here), the second step led to virtually no improvement for high and low, while the quality for close even deteriorated somewhat. I am considering modifying the second step so that only high or low but not close are changed.

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Last Updated ( Wednesday, 03 February 2010 18:22 )