I am trying to use a LSTM model to predict d+2 and d+3 closing prices. I am not sure whether I should normalize the data

  • with a MixMax scaler (-1,+1)

  • using the log return

  • (P(n)-P(0))/P(0) for each sample

I have tried quite a lot of source code from Github and they don't seem to converge on any technique.

  1. Log returns are symmetric compared to percentage change. Log(a/b)=log(b/a) and this (less skewness), in theory, leads to better results for most models (linear regression, neural networks).
  2. Neural networks like lstm work better if the values are close to zero, but the difference in normalizations is usually not that big.
  3. Any returns (log or percentage) are better than raw values because prices change according to previous prices. Their absolute (raw) values have almost negligible influence compared to previous price.

I would recommend first to convert to log returns and then normalize. If it is daily prices then I would divide the log returns by something like 0.05. Price changes have very heavy tails in a distribution so I would not suggest using minmax because then you divide by something like 0.5 (which probably was in great depression) and get all values too close to zero. Dividing by standard deviation should also be good.

But reality is different than theory, so it is better to benchmark. Maybe percentage changes are better because this is the number people see and react to. And markets are a lot about psychology.

And be prepared to see very high errors and bad models. Financial markets are badly predictable both in practice and theory. According to economic theory if they were predictable and people are rational and have unlimited credit lines then any possibility of earning additional money compared to the whole market will be closed in milliseconds. Only if you find some way to analyze data that noone is currently using only then will you be able to earn money. Neural networks were discussed in 1990s to predict financial markets. So LSTM is not really new in 2018.

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