A nice implementation of polynomial smoothing in R is provided by the KernSmooth package. The package contains the dpill() function, which helps to select the bandwidth of a local linear Gaussian kernel regression estimate. A small bandwidth means less smoothing, and a large bandwidth means more smoothing

The package includes the locpoly() function, which constructs a polynomial that is fitted to the near-by data points around each data point. The resulting local polynomials create a smoothed version of the original data series.

Both, the dpill() and locpoly() function require to specify number of points (gridsize) for which a local polynomial is constructed.

library(KernSmooth)
library(xts)
load(url("https://userpage.fu-berlin.de/soga/data/r-data/Earth_Surface_Temperature.RData"))

dt <- index(temp_global)
y <- coredata(temp_global)
gridsize <- length(dt) / 12 # evaluate local polynomial annually (12 months)

# estimate bandwidth of a local linear Gaussian kernel
bandwidth <- dpill(dt, y, gridsize = gridsize)
bandwidth

## [1] 2.947308

# Function estimation using local polynomials
lp <- locpoly(x = dt, y = y, bandwidth = bandwidth, gridsize = gridsize)

### PLOTTING ###
plot(dt, y, type = "l", col = "gray", xlab = "", ylab = "", main = "Smoothing via local polynomials")

lines(lp, col = "red", type = "l")

legend("topleft", legend = paste0("bbandwidth = ", round(bandwidth, 2)), col = "red", lty = 1, cex = 0.6)

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Citation

The E-Learning project SOGA-R was developed at the Department of Earth Sciences by Kai Hartmann, Joachim Krois and Annette Rudolph. You can reach us via mail by soga[at]zedat.fu-berlin.de.

You may use this project freely under the Creative Commons Attribution-ShareAlike 4.0 International License.

Please cite as follow: Hartmann, K., Krois, J., Rudolph, A. (2023): Statistics and Geodata Analysis using R (SOGA-R). Department of Earth Sciences, Freie Universitaet Berlin.