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, 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.

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.