R 具有高斯分布的加权平均值

Question

Limited stats education, so possibly am trying to define something that is a simple function, or why I am unable to find an existing answer

The problem is to calculate a weighted mean for a time series, with greater weight to the most recent data. The weighting should follow "one side of a gaussian curve" function ("S" curve?), highest value starting from the most recent (last) point. I realise there would be a couple coefficients to define the gradient of the curve, but assume "normal"

Weighting Points along an 'S' curve in R

This seems to be asking the same question, but the only answer is a bit over-engineered for what I am looking for

I can generate a linear weighted average as follows

# time series data
d <- c(7, 8, 10, 7, 8, 11, 9, 6, 13, 10, 11, 11)
# weight coefficients
w <- seq(1, length(d), 1)
w <- w / sum(w)
w
[1] 0.01282051 0.02564103 0.03846154 0.05128205 0.06410256 0.07692308 0.08974359 0.10256410
[9] 0.11538462 0.12820513 0.14102564 0.15384615
weighted.mean(d, w, na.rm = T)
[1] 9.846154

How do I use a "gaussian sequence" for w instead of my linear one?

Answer 1

You can get weights that follow the left-hand side of a normal distribution like this:

w <- dnorm(seq(-3, 0, length = length(d)))
w <- w / sum(w)

So the weights look something like this:

plot(w)

If you want the curve to be steeper, you can set the sd argument of dnorm to less than 1, and if you want it more gradual, increase its value. At the moment the example shows the default, with sd = 1.

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EDIT

An alternative that might allow for better control would be a logistic curve:

w <- plogis(seq(-1, 1, length = length(d)), scale = 0.3)
w <- w / sum(w)
plot(w)

w <- plogis(seq(-1, 1, length = length(d)), scale = 0.15)
w <- w / sum(w)
plot(w)

Answer 2

To run a weighted mean along a time series, I would recommend using convolve for efficiency reason, rather than trying to reimplement it. For instance:

d <- c(7, 8, 10, 7, 8, 11, 9, 6, 13, 10, 11, 11)

k <- dnorm(seq(-2,2, length.out = 5))

convolve(d, k/sum(k), type = "filter")


[1]  9.466427  7.427122  8.213693 10.465371  8.894341  7.066883 11.933909
[8] 10.425011