# Ensemble Estimators

For more advanced users, the NeuroShell Trader can easily implement “ensemble estimators”, wherein several predictions or estimations are then fed into a higher level prediction or estimator for the final answer. In this way, the higher level estimator acts like a supervisor who queries his/her employees for their projections before producing his/her own.

To implement an “averaging” ensemble prediction, first use the Prediction Wizard to build three predictions, all based upon different inputs. Then use the Average3 indicator to average the three results:

Average3(prediction signal 1, prediction signal 2, prediction signal 3)

To implement a “supervisory” ensemble prediction, again use the Prediction Wizard to build three predictions, all based upon different inputs. Then use the Prediction Wizard to build a new prediction whose inputs are the three prediction signals.

To implement a “consensus” ensemble trading strategy (a.k.a. a panel of experts), build three rules (made up of predictions or a combination of predictions and indicators). In the Trading Strategy Wizard, insert the three rules for long entry, e.g.:

A>B(Prediction signal 1, 0)
BB High Breakout(Close, 20, 2)
CloseAvg>OpenAvg(Open, Close, 5)

In the Trading Strategy Wizard, specify that the buy signal should be generated if two of the conditions are true. Make similar rules for long exit, again specifying signal generation upon two of the three rules being true.

If you have the NeuroShell Trader Professional, you can optimize the three rules above.

For short entries, you may want unanimous agreement, so specify that all conditions be true.

It is easy to prove that consensus models (independent ones) work better than any of their parts if you think of your models at any time as being either right or wrong, as say in a reversal strategy where you are either long or short. Let’s say you have three models (A, B, and C) and each one has a probability of 0.6 of being correct at any given time. In other words, the models are 60% right. To figure the probability that the average (which is the consensus) is right, think of it this way. The average is right if 2 or 3 of the 3 are right. Now,

probability of A right, B right, C wrong = 0.6 x 0.6 x 0.4 = 0.144
probability of A right, B wrong, C right = 0.6 x 0.4 x 0.6 = 0.144
probability of A wrong, B right, C right = 0.4 x 0.6 x 0.6 = 0.144
probability of A right, B right, C right = 0.6 x 0.6 x 0.6 = 0.216

The sum of the probabilities is 0.648 so the average will be right about 64.8% of the time.

If you assume the models are 55% right, the average of the 3 is 57.475% right.

You can simulate this in an Excel spreadsheet and the numbers should come out pretty close.