# Non-overlapping ranges of HCNN' observables and of state transition function

In the artcicle Forecasting and Trading the High-Low Range of Stocks and ETFs with Neural Networks HCNN is used for forecasting of nine time-series, namely:

• returns of the lows
• returns of the highs
• five-period exponential moving average of the lows
• five-period exponential moving average of the highs
• five-period lower bollinger band of the closes
• five-period upper bollinger band of the closes
• returns of the open
• same-day return open to low
• same-day return open to high

The proposed state transition function is: $$s_{t+1}=\tanh(W \cdot s_t)$$ The outputs (predictions) of HCNN are the first nine elements of state vector $s_{t+1}$ so the outputs are within the range $[-1,1]$. The questions are:

1. Would it be correct to assume that "returns on ..." are represented as negative and positive deltas, i.e. 10% increase in price is 0.1 while 5% loss is -0.05?
2. Five-period exponential moving average of lows will be in general well beyound $[-1,1]$ range of $\tanh$. Shouldn't these values be scaled into the $[-1,1]$ range? How?