Standard deviation indicator?

AmericanNinja · June 13, 2014, 3:05am

Does anyone have the mql4 files for these indis? I’d like to incorporate the Z-score indi into my pairs trading EA. I would appreciate this very much.

Mata_Nui:

They are quite simple really, as you see i have given you the mql files so you can have a proper look yourself but I spent quite a bit of time researching cointegration and Z scores before creating these. I guess you will have had a look as well and found most of the stuff on the web is pretty math intensive and because its all written for academic use there are not any examples that are very easy to follow. What i discovered though is that most of the difficult stuff is about finding how cointegrated pairs are (to find profitable pairings). The actual measurement of if they are following that model is pretty simple. Also i wanted something that would just fit onto an mt4 chart so it had to be basic. So this is how i did it:

First find the spread between the 2 selected instruments. There are a few ways you can do it, you can subtract one from the other (As its MT4 charts use the close of the bar), divide one by the other or one example i saw used logs of each close price. It doesnt matter really, i tried them all and the graph looks EXACTLY the same in each case. So these indicators besides the percentage one which i will explain later use the close of instrument1/close of instrument2 to find the spread. - This gives us a value for current spread at close of that bar.

Then find the average spread. I do this by using the MAOnArray function in MT4 to find the moving average over 100 periods of the spread. - So we now have the current spread and an average spread.

Then find the Std Dev for the same period. MT4 has a function for StdDevOnArray so i just plug the same array into that to find the Std Dev over our 100 period average. - So we now have the current spread, an average spread and the Std Deviation.

I could have plotted those as they are but i would have ended up with wavey lines on top of wavey lines and it wouldnt look too good. I know this because i had experimented with plotting the average and current then applying b-bands to the average. It worked (sort of) but was a mess to look at. Since i only really needed to know how many deviations from the mean the current spread is i used the following formula to kind of normalize it against a 0 axis.
z = (diff-mean)/stDev

Then i just plot z.

I have no idea if this is how it should be done and only have high school maths (OK, slightly better since i am a programmer but its not something i have really done before) but it does seem to show what it is meant to show. I am sure it could be improved on though.

The percentage indicator is similar but it doesnt use the difference in close prices directly. It looks at relative movement. So it compares how far each instrument has moved since the open of the day bar as a percentage of that open value. As you can see the chart is the same. I did it as an experiment really. I thought it might work better for comparing currency and index values (so GBPUSD and FTSE for example) but it doesnt make much difference.

Mata_Nui · June 13, 2014, 4:40am

Post #5, Indicators.zip. Its got the MQL files.

AmericanNinja · June 13, 2014, 5:32pm

Hi Mata Nui,
I downloaded the zip in post #5. It contains the ex4 files (which i appreciate very much). Would you be willing to share the mql4 source code files?

AmericanNinja · June 14, 2014, 8:49pm

Does anyone have the actual mql4 code for these indicators?

Mata_Nui · June 16, 2014, 9:24am

Indicators and MQL. They were created on build 509.

AmericanNinja · June 16, 2014, 10:20pm

Thanks Mata Nui! I appreciate them very much. If you have any interest in continued development and possibly trading with these and other indicators in a statistical arbitrage system, I’d be open to discussing a few ideas with you. Your code looks excellent. I am a programmer as well and have quite a bit of experience with stat arb trading using cointegration. I did find one small error in the way the mean and StDev are being calculated. If you’d like to discuss it let me know. I could also just apply the fix (as I understand it) and send you the code. Thanks again.

Mata_Nui · June 17, 2014, 4:48am

I am not a mathematician so i had to do a lot of hunting around to get that far. What changes would you make to the mean and stdev? I haven’t looked at this code for a while but looking at it now i see a bit i am not sure is correct.

Have you traded stat arb before? The main problem i found with these indicators (and statarb in general) is that you are always using a mean of some sort. Obviously the point of it is that price deviates from that mean then reverts. The issue is though that if the move continues for a while then rather than the price difference reverting to the mean (profit), the mean changes to move closer to the current price difference (resulting in loss). I couldnt find a way around this. Obviously if you have any ideas on effective use of these indicators i would be interested.