# Prepare dummy data.frame
set.seed(2222)
lonlat <- expand.grid(1:10, 1:10)
df <- data.frame( lon = lonlat[, 1],
                  lat = lonlat[, 2],
                  ANNUAL_MEAN = rnorm(100),
                  ANNUAL_RANGE = runif(100, 1, 5)
                )

library(raster)

# Convert data frame to raster object
rdf <- df
coordinates(rdf) <- ~ lon + lat
gridded(rdf) <- TRUE
rdf <- brick(rdf) # our raster brick

## Perform moving window averaging

# prepare weights matrix (5*5)
w <- matrix(1, ncol = 5, nrow = 5)

# perform moving window averaging
ANNUAL_MEAN_AVG <- focal(rdf[[1]], w, mean, pad = TRUE, na.rm = TRUE)
ANNUAL_RANGE_AVG <- focal(rdf[[2]], w, mean, pad = TRUE, na.rm = TRUE)

# Append new data to initial data.frame
df$ANNUAL_MEAN_AVG <- as.data.frame(ANNUAL_MEAN_AVG)
df$ANNUAL_RANGE_AVG <- as.data.frame(ANNUAL_RANGE_AVG)