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For a time series forecasting problem, I noticed some people tried to predict the difference or the quotient. For instance, in trading, we can try to predict the price difference P_{t-1} - P_t or the price quotient P_{t-1}/P_t. So we get a more stationary problem. With a recurrent neural network for a regression problem, trying to predict the price difference can be a real pain if the price does not change sufficiently fast because it will predict mostly zero at each step.

Questions :

1. What are the advantages and inconveniences of using the difference or the quotient instead of the whole quantity?


2. What can a nice tool to get rid of the repetitive zeros in a problem like trying to predict the price movement?

• If the assumption is that the price is stationary (*P_t=C^te), then predict the whole quantity.


• If the assumption is that the price increase ()is stationary (P_t= P_t-1+C^te), then predict the absolute difference P_t-P_t-1. (Note: thie is the ARIMA model with a degree of differencing=1)


• If the assumption is that the price growth (in percentage) is stationary (P_t=P_t-1 +C^te * P_t-1), then predict the relative difference P_t/P_t-1.


• If the price changes rarely (i.e. the absolute or relative difference is most often zero), then try to predict the time interval between tow changes rather than the price itself.