Is there a data decay method that decays data based on how much new data it receives?

Question

So here's the situation: There are n balls. Each ball has been voted on a scale of 1-N by an arbitrary number of people.

Every day (or every week, or more), some/most/all of the previous voters and some new voters are able to vote on the balls again. The thing is, I don't want all previous votes to all disappear because the votes that were valid yesterday are still valid today. The re-votes/new votes will just be weighted "more".

There can be more OR fewer people who vote during the new voting session.

What is a good method of data decay for this? I have thought of taking the square root of "yesterday"'s votes every day/week, but that doesn't seem like it would work well if I have lots of voters in one day because the square root of the sum of the votes doesn't decay that "much" and if I have few voters, the square root of the sum of the votes can decay less and so the new, initial votes, will skew the result set. I could be wrong; I'm not sure.

Answer 1

The EWMA (Exponentially Weighted Moving Average) is an alternative. Newer observations receive higher weigths than olders ones depending on the decay factor $\lambda \epsilon [0,1]$

$ \bar{X}_t = (1-\lambda) X_{t-1} + \lambda \bar{X}_{t-1}$

To start the recursion, an starting value $X_0$ is required, depending on each case, this can be a mean over an "initializing" period. From this formula it's not clear why this is an exponential weight but this can be shown mathematically by replacing $\bar{X}_{t-1}$ (and so on) by the very same formula until expressing $\bar{X}_{t}$ as function of {$X_0,X_1, ...,X_{t-1}$}.

You will find applications for volatility estimation of financial returns.