bomsoi2001: Southern Oscillation Index Data

Description

The Southern Oscillation Index (SOI) is the difference in barometric pressure at sea level between Tahiti and Darwin. Annual SOI and Australian rainfall data, for the years 1900-2001, are given. Australia's annual mean rainfall is an area-weighted average of the total annual precipitation at approximately 370 rainfall stations around the country.

Usage

bomsoi2001

Arguments

source

Australian Bureau of Meteorology web pages:

http://www.bom.gov.au/climate/change/rain02.txt and http://www.bom.gov.au/climate/current/soihtm1.shtml

References

Nicholls, N., Lavery, B., Frederiksen, C. and Drosdowsky, W. 1996. Recent apparent changes in relationships between the El Nino -- southern oscillation and Australian rainfall and temperature. Geophysical Research Letters 23: 3357-3360.

Examples

Run this code

bomsoi <- bomsoi2001
plot(ts(bomsoi[, 15:14], start=1900),
     panel=function(y,...)panel.smooth(1900:2001, y,...))
pause()

# Check for skewness by comparing the normal probability plots for 
# different a, e.g.
par(mfrow = c(2,3))
for (a in c(50, 100, 150, 200, 250, 300))
qqnorm(log(bomsoi[, "avrain"] - a))
  # a = 250 leads to a nearly linear plot

pause()

par(mfrow = c(1,1))
plot(bomsoi$SOI, log(bomsoi$avrain - 250), xlab = "SOI",
     ylab = "log(avrain = 250)")
lines(lowess(bomsoi$SOI)$y, lowess(log(bomsoi$avrain - 250))$y, lwd=2)
  # NB: separate lowess fits against time
lines(lowess(bomsoi$SOI, log(bomsoi$avrain - 250)))
pause()

xbomsoi <-
  with(bomsoi, data.frame(SOI=SOI, cuberootRain=avrain^0.33))
xbomsoi$trendSOI <- lowess(xbomsoi$SOI)$y
xbomsoi$trendRain <- lowess(xbomsoi$cuberootRain)$y
rainpos <- pretty(bomsoi$avrain, 5)
with(xbomsoi,
     {plot(cuberootRain ~ SOI, xlab = "SOI",
           ylab = "Rainfall (cube root scale)", yaxt="n")
     axis(2, at = rainpos^0.33, labels=paste(rainpos))
## Relative changes in the two trend curves
     lines(lowess(cuberootRain ~ SOI))
     lines(lowess(trendRain ~ trendSOI), lwd=2)
  })
pause()

xbomsoi$detrendRain <-
  with(xbomsoi, cuberootRain - trendRain + mean(trendRain))
xbomsoi$detrendSOI <-
  with(xbomsoi, SOI - trendSOI + mean(trendSOI))
oldpar <- par(mfrow=c(1,2), pty="s")
plot(cuberootRain ~ SOI, data = xbomsoi,
     ylab = "Rainfall (cube root scale)", yaxt="n")
axis(2, at = rainpos^0.33, labels=paste(rainpos))
with(xbomsoi, lines(lowess(cuberootRain ~ SOI)))
plot(detrendRain ~ detrendSOI, data = xbomsoi,
  xlab="Detrended SOI", ylab = "Detrended rainfall", yaxt="n")
axis(2, at = rainpos^0.33, labels=paste(rainpos))
with(xbomsoi, lines(lowess(detrendRain ~ detrendSOI)))
pause()

par(oldpar)
attach(xbomsoi)
xbomsoi.ma0 <- arima(detrendRain, xreg=detrendSOI, order=c(0,0,0))
# ordinary regression model

xbomsoi.ma12 <- arima(detrendRain, xreg=detrendSOI,
                      order=c(0,0,12))
# regression with MA(12) errors -- all 12 MA parameters are estimated
xbomsoi.ma12
pause()

xbomsoi.ma12s <- arima(detrendRain, xreg=detrendSOI,
                      seasonal=list(order=c(0,0,1), period=12))
# regression with seasonal MA(1) (lag 12) errors -- only 1 MA parameter
# is estimated
xbomsoi.ma12s
pause()

xbomsoi.maSel <- arima(x = detrendRain, order = c(0, 0, 12),
                        xreg = detrendSOI, fixed = c(0, 0, 0,
                        NA, rep(0, 4), NA, 0, NA, NA, NA, NA),
                        transform.pars=FALSE)
# error term is MA(12) with fixed 0's at lags 1, 2, 3, 5, 6, 7, 8, 10
# NA's are used to designate coefficients that still need to be estimated
# transform.pars is set to FALSE, so that MA coefficients are not
# transformed (see help(arima))

detach(xbomsoi)
pause()

Box.test(resid(lm(detrendRain ~ detrendSOI, data = xbomsoi)),
          type="Ljung-Box", lag=20)

pause()

attach(xbomsoi)
 xbomsoi2.maSel <- arima(x = detrendRain, order = c(0, 0, 12),
                         xreg = poly(detrendSOI,2), fixed = c(0,
                         0, 0, NA, rep(0, 4), NA, 0, rep(NA,5)),
                         transform.pars=FALSE)
 xbomsoi2.maSel
qqnorm(resid(xbomsoi.maSel, type="normalized"))
detach(xbomsoi)