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

Answer 3

I too get errors from Hmisc when using the wtd.var() function. Fortunately, SDMTools has comparable functionality, and even calculates SD directly for you, without needing to take sqrt of variance.

library(SDMTools)

x <- c(3.7,3.3,3.5,2.8)
wt <- c(5,  5,  4,  1)/15  ## Note: no actual need to normalize weights to sum to 1, this will be done automatically.

wt.mean(x, wt)
wt.sd(x,wt)

wt.var(x, wt)

Answer 4

Hmisc package provides this functionality:

http://rgm2.lab.nig.ac.jp/RGM2/func.php?rd_id=Hmisc:wtd.stats