# The first time you use R (and perhaps after that as well) you will want to enter these three commands:
install.packages("astsa")
require(astsa)
help(package = astsa) 

# birth is an included series


# If the times were not alrready included one could add them:
# birth = ts(birth, frequency = 12, start = 1948)
# to get years, rather than months, as the units

## Compute a centred moving average:
ma = filter(birth, sides=2, c(.5, rep(1,11), .5)/12)  # moving average 

## To better undersand what this command does, look at the vector c(.5, rep(1,11), .5):
c(.5, rep(1,11), .5)

## Make some plots:
par(mfrow=c(2,1))  # A 2 by 1 panel of plots
plot(birth, main="births")
plot(ma, ylim=c(min(birth),max(birth)), main="moving average")

# now try this:  
win.graph()
par(mfrow=c(2,1))
ts.plot(birth, ma, lty=2:1, col=1:2, lwd=1:2, main="births with moving average superimposed")
residuals = birth - ma
plot(residuals, main = "residuals from moving average")