CurrDayChange input and the general bullishness in that lookback period. Has currDayChange really a genuine differentiation power?

11May11

Is success of the currDayChange input due to the lucky selection of 200 days lookback and the general bullishness/bearishness in that period?

Let’s suppose a simple case: In the last 200 days, the average of nextDay%Change of the Up and also the Down days were positive. For example, because we are in a generally bullish period. That can easily happen. Just take a look how long the RUT/SPX can stay above the SMA(200). How will the deterministic 2bins naive learner decide? It should vote positively for both Up and for Down days. There is no daily MR, no daily FT.
In that case, it is very likely (not assured, because the NN is not a 2bins forecaster, but continuous), that the NN will cast an Up day irrespective of the input, the currDayChange. Does the success (30% CAGR) of the NN, because it correctly just says that it is a generally bullish market?
The answer:
No.

We prove here that if we project generally an Up vote for next day, irrespective of the input currDayChange, we will have no phenomenal results.
To prove it, instead of using a 2bins Naive Learner, or a 4bins NR that we used earlier, we use a 1bins Naive Learner. (What a great idea! How could we miss testing it earlier?) This will aggregate all the outputs in the previous 200 days period to simply to an average number.
The sign of that average will determine the next day forecast.

Let’s see the PV, CAGR and dStat values that compares the
– Buy&Hold,
– daily Mean Reversion
– daily Follow Through
– 1bin Naive Learner
– 2bins Naive Learner
– 4bins Naive Learner
– Stochastic Neural Network:

Conclusion:
As you can see, the adaptive Naive Learner gained nothing, not too much (5% CAGR) if it only considered the average nextDayChanges during that 200 days (1bin case).
However, it has genuine prediction power (27% CAGR) if it distinguishes current Up days from current Down days. (2 bins case).

So, we can contend that the currDayChange as an input is a very good input. Probably, we are too lucky with this input, because it has such a strong correlation to the output.

The goodness of currDayChange input is really because of the nature of it (either MR or FT days), and not because there is a general bullish/bearish trend in the previous 200 days.
In general, we expect that each of our input (per se) has only weak correlation to the output, and the aggregation of many inputs, many weak prediction power inputs will give us an edge in the form of the ‘input-combined’ Neural Network.

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