### FXE (Euro) input, ensemble of 11

subject: FXE (Euro) input, ensemble of 11

**This is the continuation of a previous post** (see here), in which we studied the discretization of the **FXE input. Our previous backtest was performed without ensembles**, so our backtests were very volatile.

We have only **1 input now, the FXE current day return**. We try to discretize the input into different equal sample size bins. Presenting the data in a nice simple way, we increase the chance that the ANN can learn it. **We backtest 6 years now.**

The parameters of the experiments:

`nNeurons = 2;`

nEpoch = 10;

lookbackWindowSize = 200;

outlierFixLimit = 0.04;

nEnsembleMembers = [11, 0, 0];

note that **we increased the nEpoch from 5 to 10**, because in a previous test, it turned out that it is advantageous.

We made 8 different random experiments.

the non-discretized experiments:

Note the STD here. The 2bins case is very stable. Almost all the experiments give the same result. This is the beauty of discretization. We made the objective function simple. The ANN can learn it easily and consistently. Compare that STD with the STD of the continuous case.

The performance numbers in one table:

And we make a plot of these performance numbers.

We preset a plot of TR for the continuous case. The ANN has to learn the positive and negative correlations between the FXE and the RUT over the years, as it was discussed in the previous post.

Conclusions:

– **This is a surprise result. This test revealed that it is not advantageous to discretize the input.** **This is the opposite result that we got for the CurrDayChange discretization case. For that input even the simplest discretization (2 bins) was better than the continuous version.**

– **the highest D_stat (53.09%) and the highest TR (71.43%) are in the continuous case**. (however, note the STD increases as we increase the bins, and it shows high randomness). This show that **there is some important information that we lose if we discretize** and the ANN could have use that information. At first, we think that t**here may be some outliers in the FXE return input and those are the important information that we erased.** However, this needs to be proved.

– **compare this performance to the performance of the 1 member ensemble case:**

In this **11 member ensemble version, by and large the performance measures are better compared to the 1 ensemble case.** For example in **the continuous version, the CAGR improved from 13.7% to 20.75% and the TR improved from 39% to 71%. (The backtest is performed for 6 years.)**

– **Personally, I would love to use the 6 bins version** (maybe with more nNeurons). Intuitively it feels right to discretize the today change as very oversold, oversold, slightly oversold, slightly overbought, overbought, very overbought. I like these 6 categories. However, **the 6 bins case gave the worst result.**

– The 2 bins case has the lowest randomness. If that is important: stability (for backtest), low nEnsembleMembers, use the 2 bins case. And **the 2 bins case gave a decent result too. If I don’t count the continuous case (the result is maybe some aberration, outliers, etc.), the 2 bins case gives the best result. I guess we will use that in the future. **

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