Discounting Old Time Series Values, Exponential Smoothing

Question

I would like to build a time series from another time series, discounting older values. That is, the most recent value is included in the sum normally, and the previous value is discounted with delta^t. Then a new value is added, which is again normally included in the new time series, the older values are then discounted with delta^t and delta^(t-k). The whole thing should look like this:

Data: df<- c(0.4387738, 0.05203873, 0.3238407, 0.1117364)

> test[[1]][["se_ne"]][[1]] 
[1] 0.4387738
> 
> test[[2]][["se_ne"]][[2]] + 0.4^(2-1)*test[[2]][["se_ne"]][[2-1]] 
[1] 0.2275482
> 
> test[[3]][["se_ne"]][[3]] + 0.4^(3-2)*test[[3]][["se_ne"]][[3-1]] + 0.4^(3-1)*test[[3]][["se_ne"]][[3-2]] 
[1] 0.41486

But the dataset has over 700 observations, is there a smarter solution than calculating everything by hand?

Thanks for the feedback!

Answer 1

Perhaps this SO answer might help you:

Exponential smoothing method

If it does not, then a good next step would be to explain the differences between that post and your question.