Calculating weighted mean and standard deviation

Question

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

Answer 1

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) 

Answer 2

The Hmisc package contains the functions you need.

Thus:

x <- c(3.7,3.3,3.5,2.8)  wt <- c(5,  5,  4,  1)/15  xm <- wtd.mean(x, wt)  var <- wtd.var(x, wt)  sd <- sqrt(var) 

Unfortunately the author of the Hmisc package did not include an explicit wtd.sd function. You have to square root wtd.var.

Charles Kangai