

Prediction quality for high, low is improved by tying the four components of a day candle together. 
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.
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 halfwidth 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 pricerelated quantities: the logarithmic returns of high, low, and close. Due to 24hour 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:
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 lowhigh 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. 

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