Danica v0.5 forecast does not "age" intra-day, is more relevant to periods of high volatility.

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Written by Forex Automaton   
Monday, 22 March 2010 17:29
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Danica v0.5 forecast does not "age" intra-day, is more relevant to periods of high volatility.
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So far, positive Pearson correlation coefficients between system forecasts and real forex moves on the day scale have been seen both during the back testing and in the live regime and it looks like a positive expectancy trading system has been indeed created. Among the methods of risk management, we have been focusing our effors on the issues of what forecasts to trade and how to allocate capital to trades. This report is our first research attempt to reduce risk by being selective about when to trade during the day.

The philosophy and motivation behind using Pearson correlation coefficient as a measure of potential system trading returns has been discussed most recently in the February performance report. What has never been looked at though is how the success of the forecast (or lack thereof) is distributed in time. Meanwhile, if the distribution is non-uniform, the operator will benefit from being exposed to the market during the hours when the positive expectancy is at its best, and does not want to be exposed to the market when the expectancy is zero or negative. In this post, I present and discuss data on the temporal structure of the net positive correlation between the reality and forecast on the day scale.

The quantities whose statistics we are going to look at are similar to Pearson correlation coefficient but lack normalization (or in other words, they lack the procedure which limits variation of Pearson correlation coefficient to the -1,+1 range). This makes them simpler; normalization is not needed in this case since we do want to look at the information it removes, namely the information about variations in volatility during the day.

In this report, the analysis is limited to looking at two quantities. First is the product of the daily predicted return and hourly actual returns during the day

[f(t)/f(t-24)-1][p(t-i)/p(t-i-1)-1], i=0,1,2,...,23, time t is expressed in hours,

p denotes the actual exchange rate quote and f denotes its forecast.

The second quantity is a volatility measure

[p(t-i)/p(t-i-1)-1]2, i=0,1,2,...,23, time t is in expressed in hours.

The computational part of the analysis consists in histogramming and characterizing the distributions of these two quantities. The distributions are characterized by a mean and a second moment (RMS). Due to the fact that the mean of [p(t-i)/p(t-i-1)-1] is very small, the mean of [p(t-i)/p(t-i-1)-1]2 is a close approximation of variance and will be called that way.

Danica v0.5 refers to the version of the system available as of January 14, 2010. This version contains significant improvements compared to earlier versions (the system went through several of them during the back-testing) whose output is stored in the archive.

Product of predicted relative move for the day and the actual relative move during the hour for 14 forex rates as a 2-dimensional distribution. 1.1 Product of predicted relative move for the day and the actual relative move during the hour for 14 forex rates as a profile histogram 1.2 Variance of actual relative move during the hour 1.3

Fig.1. Intraday study of day-scale Danica v0.5 forecast. Central European time (CET) is used on the axis. 9am Eastern time, the moment when the forecast is generated, corresponds to 15:00 (3pm) CET. 1.1: product of predicted relative exchange rate move for the day (from 9am Eastern time to 9am Eastern time) and the actual move during each of the hours, with respect to the previous hour. 1.2: same as above, but in profile representation. L0 refers to the trigger word 3 of the L0 trigger the essence of which is the requirement of a coincidence in forecast directions for the upcoming day's high, low, and close. 1.3: variance, or rather the second power of the actual relative hour-by-hour move in the quote, showing the intra-day volatility pattern. The points in profile plots 1.2 and 1.3 mark the mean values while the width of hatched band at every point is twice the RMS of the distribution.

Tokyo 9 1011 1213 14 15 16 17 18 19 20 21 2223 0 1 2 3 4 5 6 7 8
Central Europe 123456789101112 13141516171819202122230
Greenwich 01234567891011 121314151617181920212223
Eastern US 19202122230123456 789101112131415161718

Table 1. Time zone conversion table. Seasonal time shifts, such as daylight saving time, may complicate the picture if the nations choose to enact them on different days, and are ignored.

The top panel of Fig.1 is useful only as an educational illustration; it demonstrates the degree of numerical sophistication it takes to extract the output from the data. Visual analysis of Fig.1.1 gives little but it does alert the reader to the broadness of the distribution. It also indicates the areas of higher and lower volatility. One can tell the volatility is higher where the hight of the "ridge" is lower, since volatility redistributes the data on the slopes away from zero.

Profile representation, Fig.1.2, shows position of the mean and the RMS of each of the one-hour slices in Fig.1.1. Magnitude of the quantity plotted along the vertical axis in Fig.1.2 is most important here. As follows from definition, the quantity measures the degree of "relevance" of the forecast to the actual price moves within each of the subsequent 24 hours. The forecast is issued at 15:00 in the time units used in the figure and the 15:00 point itself measures the relevance of the previous day forecast to the hour ending at 15:00.

Some conclusions from Fig.1.2 and 1.3 are:

  • The shape in Fig.1.2 resembles that of Fig.1.3. In other words, success of system trading correlates with volatility: the most successful hours of system operation fall within the period of high market activity in London and New York.

  • The 19-hour time span between the moment of time the forecast is generated (15:00 CET) and the peak of trading activity in Europe (10:00 CET) does not prevent yesterday's forecast from being relevant. For all we care, the market may very well be in random walk mode during the period which can be described as Central European night, and yet as soon as the activity returns in the morning, it returns in a way which is net-beneficial to the Danica user.

Given this evidence, the best method of operation seems to be: when the forecast is generated at 9am Eastern time (15:00 Central European time on the plot), one opens the positions (in accordance with the past and forthcoming research related to the forecast selection and position sizing) and keeps them open till 18:00 Central European time which is normally noon in New York. Next morning, at 10:00 Central European time, the operator enters the market acting on the same forecast, and holds until the next forecast, at which point the operator makes adjustments.

Based on the new forecast directions for the close, low and high, adjustments are made as to which positions should be kept, which should be closed, and which new ones should be opened. The new high and low for the past day give the new positions of the protective stops. If one decides to risk a fixed amount per trade as a potential loss by stop-loss, then large moves during the day that's just over will naturally limit the position size and will lead to profit taking on a fraction of the position. The 24-hour cycle repeats itself. An open question right now is whether one should re-open the positions which were closed by protective stop.

A better solution may be to run another independent day-scale trading system with the update point at 10:00 CET. However, one should not take it for granted that for such a system, the non-trivial aspects of Fig. 1 will look the same or even similar, even though it is reasonable to expect that to be the case.

As you can see, the distribution in Fig.1 leaves people in the US time zones at a disadvantage as it may be uncomfortable for them to submit orders at 10:00 CET which is 4am Eastern time (1am Pacific time).

Why simply taking profit when the profit seems "good enough" can be wrong? Here is how William Eckhardt put it in an interview given to Jack Schwager ("The New Market Wizards: Conversations with America's Top Traders"):

"One common adage on this subject that is completely wrongheaded is: You can't go broke taking profits. That's precisely how many traders do go broke. While amateurs go broke by taking large losses, professionals go broke by taking small profits. The problem in a nutshell is that human nature does not operate to maximize gain but rather to maximize the chance of a gain.

In order to be successful with discretionary profit-taking, you have to be equally successful in discretionary loss-taking. Treating profits and losses on the same footing is, for reasons of psychology, notoriously difficult for most people to do. A trading system as such is free from emotional problems but the execution is up to its operator.


Fig.1 shows aggreagated data for the 14 currency pairs tracked. This summary section is followed by 14 subsections showing the same type of plots for the individual currency pairs.

Last Updated ( Friday, 01 June 2012 16:21 )