```
# Load data set
load(url("http://had.co.nz/de.zip"))
# Figure out what we just loaded
ls()
str(de)
# Is a list consisting of 3d arrays
# - list is of difference meterological variables
# - array is 3d array of location and time
# Is meterological data on 24 x 24 grid over central America
# Data collected monthly for 6 years (72 observations total)
str(de$temperature)
# Extract single time series for experimentation
o <- de$ozone[1,1,]
plot(o, type=”l”)
# Deasonalising -----------------------------------------------
# Strong seasonal effect - how can we remove it?
# Simple way is just to take difference with lag twelve
# For each month, this will subtract the previous years value
plot(diff(o, lag=12))
# And make a function that deasonalises a single location
# This is useful because if we come up with a better way of
# deseasonalising the data (see below) we can easily plug it in
(x) diff(x, lag=12)
ds(o)
# Always check it works!
# Repeat over all locations -----------------------------------
# Now want to deasonalise all locations. Could possibility do
# this by hand but it would be fiddly and take a long time.
# Instead we'll use the iapply function which splits an array
# in to pieces, applies our function to each piece and then joins
# the pieces back together
library(reshape)
# Arguments to iapply:
# * array to manipulate
# * array indices to split up by
# * function to use
# Location stored in the first two dimensions, so we need to use
# 1:2 as the second argument
# Check that it's doing what we expect
dim(iapply(de$ozone, 1:2, ds)
str(iapply(de$ozone, 1:2, ds)
iapply(de$ozone, 1:2, ds)[1, 1, ]
# Finally, create a function to encapsulate this task
(x) iapply(x, 1:2, ds)
# Repeat for all variables ------------------------------
# Similarly want to deasonalise all locations for all variables.
# Different variables stored in a list, so we can use lapply
lapply(de, ds_all)
# Easy! :)
# Advanced deasonalising -------------------------------------
# Another approach would be to subtract each month's average value
# The easiest way to do this is with a linear model
# Need to create variable which gives month for each time point
# Use factor because we want to estimate a mean for each month
month <- factor(rep(1:12, 6), labels=c("Jan","Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"))
# Monthly averages
coef(lm(o ~ month - 1))
# Remove monthly averages
resid(lm(o ~ month))
# Then create deasonalising function
(x) resid(lm(x ~ month))
```