I can't comment as to whether or not there are any backtested Elliot systems, because I don't know any myself.
I think one of the problems with the Elliot theory (from a backtesting point of view) is that the structure of the wave is relatively abstract.
What I mean by this is that you need to define what an Elliot wave 'looks like' in order to identify them in the first place. This is subject to personal interpretation to an extent; I've seen some instances of 'Elliot Waves' that I personally don't think meet the requirement of an Elliot Wave.
The other hurdle is to actually identify the wave before it's complete, otherwise there would be no use in looking for them. In essence, you wouldn't be looking for the complete cycle, but only the beginning of the cycle.
If the cycle doesn't end up being an Elliot Wave, then what? You end up identifying patterns that aren't Elliot Waves, and some that are...
If you were to tackle the Elliot Wave backtest, it would probably be best if an Artificial Neural Network was trained to recognize 'structures' indicitave of a wave. Developing a proprietary stragegy would be difficult if you didn't have ANN programming experience, and I don't know if there are any software packages that could do this for you (maybe if you looked hard enough...).
Interesting story on the subject...
I just finished an undergraduate research project involving pattern analysis in the stock market.
I wrote an application that looked for patterns in stock market historical data. I analyzed 500 companies in total.
Whenever the application found a pattern it liked, it would 'flag' the date it found the pattern (for a given company).
I designed some charting software, and I set it up to highlight days where the system flagged patterns it liked. Green bars are 'good' buy signals, red bars are 'bad' buy signals.
As I looked at the results, I noticed that 'buy signals' sometimes came in 'chunks of three'. I've attached an example for you to look at - it's a chart of of Agilent Technologies (over the past 40 days or so).
I saw the pattern often enough to notice it, but I didn't really understand the significance of the 'three chunks'. At the time (about a week and a half ago), I didn't know about the Elliot Wave theory.
Looking at the charts now, these three 'chunks', from what I can gather, are located in Elliot Waves...maybe there is a signficance to this, maybe not...I have to look into it further.
Regards,
Brandon