I am looking for a procedure to compute an exponential weighting of returns given a half life parameter.
I ran accross a wikipedia article, can I take it unchanged an assume N(t) is the return at time t ?
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What you want to do sounds like exponential smoothing of returns. So you want to forecast a return by exponentially weighting recent returns. For exponential smoothing you can look at Hyndman's papers and the e-book or this course on page 34.
I personally don't think that this will give a good forecast! It would be much too easy by the way.
The link that you provide points to exponential decay. We had this in school when radio-active material got less and less. I would not just replace $N(t)$ in the wikipedia article but rather read about statistics e.g. using Hyndman's ressources (I know I cite him a lot ...).