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I am working with data sets of offers (1, 2, ... n) and how well they perform over many impressions.

Currently the most recent data (30 days) is used to aggregate the raw performance stats into distinct probabilities for each offer. Is there any numerical method that weights the more recent data when aggregating data, with the assumption that the most recent data is more accurate? Or is there any method that takes, say 10% the probability from the last 30 days, and 90% from the last 7 days to produce an overall probability.

Is there a name for this problem?

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I'll give you an example from finance. Let's say we get the sequence of portfolio returns $r_t$. We can compute the volatility as usual $\sigma^2=\frac{\sum_tr_t^2}{n}$, assuminhg the average return is zero.

Now, volatility is used to compute the value-at-risk of a portfolio. One could argue that the "old" returns should not be coming into the volatility calculation at the same weight as more recent observations. So, Alan White proposed to weigh the returns at time $t$ by the ratio of most recent volatility at time $N$ to the volatility of a return in the past, see Eq.(1) in this paper: $$r_{t}^*=\sigma_{N}\frac{r_{t}}{\sigma_{t}}$$

You could compute volatility using either GARCH or EWMA.

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  • $\begingroup$ So in eq 1 we would multiply the 30 day probability by the 1 day std dev over the 30 day std dev? $\endgroup$
    – hoshi
    Commented Jan 5, 2015 at 20:22
  • $\begingroup$ This is just a general idea, how exactly you may implement the weighting is up to you. In the given example volatility happens to be an important parameter. $\endgroup$
    – Aksakal
    Commented Jan 5, 2015 at 20:30

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