在 R 中为 EWMA 写一个从 0 到 n 的总和

Question

I am trying to write the following sum in R but no success so far. The sum I am trying to write is the following:

from t=0 to t=260, Rt * Lambda^t * (1-Lambda)

Rt represents the returns at time t, Lambda is a decay coefficient (=0.97 but subject to change).

I have a time series data frame and want to apply the result of this sum for every row of the data frame. this means that for any row i, t=0 and for row i-1, t=1, row i-2, t=2 and so on.

Thank you very much for the help

Answer 1

in R you do not need loops to calculate such sums. You can simply use sum :

sum(as.numeric(rt) * lambda^(seq_along(rt) - 1) * (1-lambda))

Here is some toy data:

set.seed(1)
rt <- ts(rnorm(261))
lambda <- 0.97

You can also check out the EMA function from the TTR package.