Intermarket analysis vs markets-in-isolation on day scale.

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Written by Forex Automaton   
Thursday, 18 February 2010 10:24

I am revisiting the issue of the intermarket analysis on the day scale. The conclusion from the previous report on the subject was that, the rest of the algorithm being the same, intermarket analysis gives no advantage on this time scale and simpler analysis of the isolated markets should be preferred. In this report, data on the predictability of high and low are added and a bug related to the estimation of statistical precision of the data is fixed. Nevertheless, the conclusions remain the same.

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

Fig.1. Pearson correlation of predicted and actual day-scale logarithmic returns (1.1 -- high, 1.2 -- close, 1.3 -- low) as a function of the forecasting parameter nicknamed Fred. The vertical bands indicate a measure of uncertainty, their boundaries are plus/minus one Gaussian standard deviation (precision) of the mean. 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 having to do with the curve at large rather than with individual points.

 

Money management for the individual markets

separate

joint

Pattern analysis for the individual markets

separate

Step One

Step Two

joint

test-only

Step Three

Table 1. Various modes of the trading system operation. The present report compares Step 1, the simplest of the three, with Step 3.

Day scale data for forex majors AUD/USD, EUR/USD, GBP/USD, USD/CAD, USD/CHF, USD/JPY, covering the time span from August 20, 2002 through February 5, 2010, are used in Step 3 analysis. In Step 1 analysis, 14 markets are used, including, in addition to the forex majors listed above, AUD/JPY, CHF/JPY, EUR/AUD, EUR/CHF, EUR/GBP, EUR/JPY, GBP/CHF, and GBP/JPY. The middle and half-width of the bands around the data points in Fig.1 represent the mean and its precision for the Pearson correlation coefficients, characterizing forecasting quality for the different values of the internal adjustable parameter nicknamed as Fred.

Recall that the Pearson correlation coefficent has a known range from -1 (the quantities being total opposites) to 1 (total correlation) and that way there is a scale for comparison to know what is large and what is small. A realistic expectation for a measurement like that is to lie around 0. If forex is efficient, there is no way to design a system capable of making predictions, since all available information is instantly discounted by the market, therefore yesterday's (and older) data are of no use to predict today's close: all yesterday's information has been discounted yesterday. Therefore, in such a hypothetic situation, the predicted close (or equally, its represenative in the analysis, predicted logarithmic return) and the actual one have only one choice -- to yield zero covariance and zero Pearson correlation coefficient after a proper construction of these measures for a long enough chunk of data.

As before, Fig.1 as such is free of bias -- it shows you all the possible Fred values. Absence of the "benefit of hindsight" is thus ensured on the stage of Fig.1 analysis: the statement that it is more likely for an arbitrarily chosen Fred value to result in a positive correlation between reality and forecast is based on no particular Fred value and thus no choice is made with the benefit of hindsight. The benefit of hindsight will enter the game once a single value of Fred is chosen on the basis of Fig.1.

Finally, on the subject of comparison of Step 1 and Step 3 results. The comparison is somewhat apples-to-oranges because for Step 1, 14 forex rates are used whereas for Step 3, only 6 are used. As it stands now, Step 1 gives an undeniable advantage. In an upcoming study, the 14-forex rates are going to be used in Step 3 as well, however I currently view this as a lower priority project.

The lack of advantage brought about by introducing a more complex Step 3 algorithm is not too unexpected, as my intermarket correlation studies in forex showed the non-trivial correlations to die off within one, at most two hours of time lags, while this study deals with day data. While the increased dimensionality of analysis space ensures that more potentially relevant information is tied together, it also complicates extraction of features and the signal to noise ratio does not necessarily grow. The result may very well be different with other time scales, or with thoughtfully selected combinations of forex exchange rates.

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Last Updated ( Thursday, 13 May 2010 15:50 )