wght.sum <- function(x, w, trunc=NULL) {
  # assumes n <= m
  n <- length(x)
  m <- length(w) 
  if (n == m) {
    return(sum(x*w))
  } else if (trunc == 'L') {
    return(sum(x*w[(m-n+1):m])/sum(w[(m-n+1):m]))
  } else if (trunc == 'R') {
    return(sum(x*w[1:n])/sum(w[1:n]))
  } else {
    return('error')
  }
}

smooth <- function(x, w) {
  # assumes m is odd
  n <- length(x)
  m <- length(w)
  k <- floor(m/2)
  y <- rep(0, n)
  for (i in 1:k)         y[i] <- wght.sum(x[1:(i+k)], w, 'L')
  for (i in (k+1):(n-k)) y[i] <- wght.sum(x[(i-k):(i+k)], w)
  for (i in (n-k+1):n)   y[i] <- wght.sum(x[(i-k):n], w, 'R')
  return(y)
}

x <- scan('http://www.ms.unimelb.edu.au/~s620374/timeseries/hsales.csv')
t <- seq(1973, 1996-2/12, 1/12)

plot(t, x, type='l', xlab='year', ylab='total sales',
  main='Sales of new one-family homes, USA')
y1 <- smooth(x, rep(1/7,7))
lines(t, y1, lwd=2, col='green')
y2 <- smooth(x, c(1/24, rep(1/12, 11), 1/24))
lines(t, y2, lwd=2, col='red')

z <- matrix(x - y2, nrow=12)
s <- apply(z, 1, mean)
show(s)