Lets look how the EMA system performs when backtesting it vs Buy & Hold using the DAX data of 3750 trading days. Looking at figure 1 it doesnt look very good, only a small portion of the EMAs in the range around 400 days can beat the DAX yield.
The long as well as short timewindows lie below the benchmark performance of 9.36%, only a small amount of EMAs passes this.
In figure 2 you see the performance chart of the best EMA which has a timewindow of 411 days and gives a yield of 10.2%. The EMA falls back caused by a false signal at ca day 2900 for a longer peroid, but you can see in fig. 3 it doesnt fall into the zick zack phase (which is good atleast). Afterwards it detects the downward trend and exists the investment - to return when an upward trend is there. However shortly thereafter it gives a false signal which causes the performance to fall back - and again some false signals at the 300 days, making the performance drop.
Optimal exponential moving average against yield underperformance on trading the DAX
Fig. 4 shows all 1000 Performancecurves for the EMAs in a 3D view and fig. 5 shows the same in a top view (to avoid occlusion). This can help us to find exponential moving average with the lowest yield (underperformance ;)). The backtest results look similar to the simple average results, but in a total lower level.
Now we are looking for the timewindow which has the lowest average deviaton from the index in this backtest, it is the one with 974 days. In figure 6 you can see its performance chart, opposite to the EMA411 there is no false signal at day 2900, so the performance doesnt fall behind the benchmark. It does good in signaling the downwards trend and then reinvesting into the upwards motion, but in the last days it produces false signals and falls below the buy and hold performance.