Timing short term market turns

The top plot above shows the sine wave modelled prices in white, with the Cybercycle indicator plotted in Cyan and blue. The bottom plot shows an indicator I have created to time the turns in the original, white series based upon the Cybercycle.

The basic theory behind the projected use of this indicator is simple: extract the cyclic component of price using the Cybercycle, measure the period of the cycle, and when the Cybercycle crosses its zeroline it can be anticipated that in one quarter period's time the turn will occur. This anticipated turning point is indicated when the white sawtooth line (the time elapsed since the last Cybercycle zeroline cross) reaches the three horizontal green lines (2 days before, 1 day before and the actual "turn" day counted out from the last Cybercycle zeroline cross). The white sawtooth is reset to zero each time a Cybercycle zeroline cross occurs (shown by the red lines). This indicator has been optimised using MC techniques to account for the lead/lag at different periods of the Cybercycle compared to the original input price series.

This new indicator, combined with the previously described Tukey Chart, will provide decision making input to the final system. Projected uses might be something like:

• if a Cybercycle zeroline cross occurs whilst prices are within the Tukey upper and lower contol limits, can anticipate a short term market turn in 1/4 period's time
• if prices reach either Tukey control limit at the same time the sawtooth reaches the green lines, a signal is given to take profits, take a new position etc.

These ideas will be tested on market data, along with the Tukey Charts, in due course. However for the moment I now want to work on a new idea which, if I can successfully code it, I believe will complement the above.

Monte Carlo Optimisation of Control Limits Complete

The MC optimisation of the various ucl and lcl multipliers is now complete and the "finished product" is displayed above on the same data as in the plot of post dated 16th May 2010. Simple visual comparison of the plots shows that recent adjustments to the MC methodology of selecting the ucl and lcl multipliers makes very little difference, except in the case of the lower plot of the Fisher Transformation of the Cybercycle indicator. This tells me that further work on more MC optimisation of this would probably be a waste of time, so I now consider this optimisation work to be complete.

The idea of applying control chart theory directly to market prices and derived indicators now needs to be tested on historical market data.

Monte Carlo Optimisation of Control Limits #9

The above is the optimisation of the cybercycle ucl and lcl, adjusted so that the control lines can be plotted on price bars, i.e. the yellow lines in the plot posted on 16th may below. The green and light blue boundary lines are polynomial line fits, which will be the actual multipliers used. This plot is somewhat different to that in the post of 5th May (Monte Carlo Optimisation of Control Limits #4). I put this down to the fact that at longer periods the cybercycle tends to lead prices and so the peaks/troughs in the cybercycle do not occur at the same time as those in the underlying data. The result is the upward sloping fit seen above.

Application of Tukey Chart

Above is a screen shot of current work in progress regarding Tukey Charts.

This is a shot of the continuous back-adjusted es mini contract from early January 2010 to mid May 2010, including the 1 day, 1000 point drop! The top chart shows price bars with the optimised Tukey Chart applied directly to prices (the cyan lines) and also the Tukey Chart applied to the Cybercycle* and scaled and super-imposed on price bars (the yellow lines). The price bars are blue if the price is above both outer ucls and red if below both outer lcls, white otherwise. The middle chart is the Cybercycle* with its Tukey Chart, and the lower chart is the Fisher Transformed Cybercycle* with its Tukey Chart. The ucl and lcl multipliers used for the Cybercycle* and Fisher Transformed Cybercycle* are the same as those used from testing detailed below. These are obviously available for MC optimisation in their own right and are on my "to do" list.

*see the technical papers section at http://www.mesasoftware.com for more information.

Monte Carlo Optimisation of Control Limits #8

The third, repeated MC test for periods 25 to 50 give these results: for periods 26 and 30 only the peaks and troughs occur between the ucl and lcl zones without actually entering the zones, and in each case the number of times this happened represents less than 0.01% of the total runs. At all other periods the peaks and troughs of the sine waves occur within their respective zones.

I think that to continue with MC testing on theoretical sine waves would result in diminishing value, so this third MC test will be the last on such theoretical wave forms. These last few tests have resulted in different optimised ucl and lcl multipliers for 3 "ranges" of periods: periods 14 and less, 15 to 24, and 25 and greater.

The next step will be to rewrite the indicator with these new optimised multipliers and test it on actual market prices.

Monte Carlo Optimisation of Control Limits #7

The second, repeated, MC test has been run on periods 15 to 50 inclusive giving these results: 0.2% of total runs peak/trough outside the ucl and lcl zones at period 17, 0.2% are entirely within the zones at period 18 and 0.17% are entirely within the zones at period 22. For the same reasons as outlined in post #6, the results from this test lead me to decide that the optimised multipliers tested in this test shall apply to periods 15 to 24 inclusive in the final indicator. A third repeated MC test will be run on periods 25 to 50 inclusive.

Monte Carlo Optimisation of Control Limits #6

I have now run the Monte Carlo tests of the boundary limits. The test consisted of 3000 phase randomised sine waves per period for constant periods 10 to 50 inclusive. The amplitudes of the sine waves were also randomised, up to a maximum of 20 (20*rand). This makes a total of 123,000 random sine waves. Any time the peak or trough of a sine wave occured above the resistance zone or below the support zone this was recorded. Similarly if the peak or trough of a sine wave occured between these zones without penetrating or touching them this was separately recorded. There were 683 instances (0.56 % of total runs) that peaked/troughed outside the zones, and 379 instances (0.31 %) that peaked/troughed completely within the zones without actually touching them. All of the above 683 instances occured at period 13, whilst the 379 instances were split 265/114 between periods 10/14.

Looking at the plot from post #4 it is obvious why all the failures are concentrated at the low periods, as this is the area where the plot shows most variation in the range of the multipliers. I have therefore decided that the optimised ucl and lcl multipliers that were tested in this test shall apply only to periods less than 15 in the final indicator. I shall repeat the MC test with new ucl and lcl optimised boundary multipliers for periods 15 to 50 inclusive.