I'm looking for the best method to normalize/standardize financial prices in order to use them as inputs for my neural network. As you probably know financial prices do not follow a normal distribution and you can't even know the max or min needed for the normalization as in the test set there could be a price higher or lower than the ones in the training set.
So I thought that I could standardize my datas trough a rolling window so the price standardized at time $t$ is computed as: \begin{equation} p'_{t}=\frac{p_{t}-E(p_{t-k:t})}{\sigma(p_{t-k:t})} \end{equation}
where with $p_{t-k:t}$ I mean succession of prices within the window of length k (from the period t-k to t)
Does it make sense? Is there any reasearch that I could study in deep? I've found the adaptive normalization method but it's too advanced for what I have to do (my goal is not to predict prices, so it's just an input variable that could help the model)