Calculating weighted mean and standard deviation

mean, r, statistics, weighted

Solution

R provides weighted mean. In fact, ?weighted.mean shows this example:

 ## GPA from Siegel 1994
 wt <- c(5,  5,  4,  1)/15
 x <- c(3.7,3.3,3.5,2.8)
 xm <- weighted.mean(x, wt)

One more step:

v <- sum(wt * (x - xm)^2)

Problem

I have a time series `x_0 ... x_t`. I would like to compute the exponentially weighted variance of the data. That is: ``` V = SUM{w_i*(x_i - x_bar)^2, i=1 to T} where SUM{w_i} = 1 and x_bar=SUM{w_i*x_i} ``` ref: http://en.wikipedia.org/wiki/Weighted_mean#Weighted_sample_variance The goal is to basically weight observations that are further back in time less. This is very simple to implement but I would like to use as much built in funcitonality as possible. Does anyone know what this corresponds to in R? Thanks

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