Coding and testing of AFIRMA completed

Following on from the previous post, the coding of the AFIRMA trend line using the leading function values as a proxy for the "peek into the future" values of price is complete, and I have to say that the results are quite disappointing. Using the rules outlined in the previous post it soon became obvious from cursory scanning of the equity curves that my version AFIRMA trend line did not live up to its early, potential promise. In fact the equity curves were so disappointing that I did not even bother to do the Monte Carlo permutation and bootstrap tests. The equity curves were no better than those produced by my simple benchmark suite of "systems" and the draw downs were such that I would never trade the AFIRMA as a stand alone "system," at least with the rules outlined in the previous post.

Below is a screen shot of the AFIRMA with a window length of 21 (peeks 10 days into the future) shown on the last 150 daily bars of the S&P E-mini. The red line is my version of it, with a Blackman-Harris window, and the yellow and green lines are two original versions with a Blackman and Blackman-Harris window. As can be seen, the original versions are smooth and accurately pick out major turning points whilst my version is not as smooth and gives many false signals that result in losses, even during a trending period.

Simple analysis of this chart, knowing the reasoning and coding behind it, shows why my version fails as a directional system. Each time the price moves contrary to any immediately prevailing trend, even those of short duration, the leading functions project this small movement as if it were the turning point of a major cycle and hence one ends up with trades in the opposite direction of the major trend, the result being that one is whipsawed in and out of this major trend. My version of the AFIRMA is simply too sensitive to minor price direction changes and I do not really have an idea as to how I can dampen this sensitivity. Smoothing it would probably be pointless as one might as well just smooth the prices directly.

However, all is not completely lost. The fact that my AFIRMA is so sensitive could be useful in identifying pullbacks in trends, acting as a set up to add to positions or for continuation trades. This is something I may investigate in the future, and this idea has been added to my "to do" list. For the moment I do not think that working more on the AFIRMA would be productive.

For interest, this second chart shows AFIRMA trend lines with a window length of nine (peeks four days into the future). It can be seen that my version of AFIRMA is quite robust in that the two trend lines (this chart and the one above) have different length windows but are almost identical.

Exploratory AFIRMA trend line tests completed

As per my previous post, the exploratory tests of the AFIRMA trend line are now complete and the results are amazing. The tests in question were:

• a Monte Carlo permutation test to accept or reject the null hypothesis that the results of the AFIRMA "system" are no better than could be expected from a random re-ordering of the system's position vector
• a Monte Carlo bootstrap test to accept or reject the null hypothesis that the returns of the AFIRMA "system" are randomly centred around a zero return

Both the above tests are those that are described in Aronson's Evidence Based Technical Analysis and the AFIRMA passed both tests on all historical data series it was tested on, with the exception of the Dollar Index contract, with a p-value of zero. I suspect that it failed on the Dollar Index because of errors in the data I have for this contract. The AFIRMA that was tested had a window length of 9, which means that it "peeks into the future" for 4 bars, and a Blackman windowing function was used. The rules were quite simple: if the current bar's AFIRMA value is greater than that for the previous bar, go long at the open of the next bar or remain long if already so; and the reverse logic for shorts. No money management or stops were employed - it is a pure, one contract, always in the market test. The tests were conducted on daily bars covering the period from March 2001 to last week. The number crunching was done in Octave.

The next test was a simple visual check of the tick return equity, a simple plot of the cumulative number of ticks that the "system" would have returned. For this no allowance was made for commissions and slippage and a typical plot is shown below. This happens to be the S&P E-mini contract.


The AFIRMA is the blue line and the other lines are a simple benchmark suite I knocked up for comparative purposes, the benchmarks being

• the equivalent of a buy and hold strategy
  
• price closing above/below the 20 period simple moving average
• price closing above/below the 50 period simple moving average
• crossovers of the 20 and 50 period moving averages
• a Donchian breakout system with a parameter of 20 periods to enter and 10 to exit

This second chart was created in R using the PerformanceAnalytics package and shows the log return equity, the daily log returns and the draw downs of the above, the AFIRMA being the dark blue lines, labelled V2 in the legend.


This final shot is a screen capture of the R session, using RStudio, used to create the performance summary chart. This was the first time I had used RStudio, and I am quite impressed with it.


In summary I can say that the AFIRMA has passed the above tests sufficiently well that I am going to code the AFIRMA using the leading functions as described in my previous post.