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

bomsoi

Format

This data frame contains the following columns:

Year

a numeric vector

Jan

average January SOI values for each year

Feb

average February SOI values for each year

Mar

average March SOI values for each year

Apr

average April SOI values for each year

May

average May SOI values for each year

Jun

average June SOI values for each year

Jul

average July SOI values for each year

Aug

average August SOI values for each year

Sep

average September SOI values for each year

Oct

average October SOI values for each year

Nov

average November SOI values for each year

Dec

average December SOI values for each year

SOI

a numeric vector consisting of average annual SOI values

avrain

a numeric vector consisting of a weighted average annual rainfall at a large number of Australian sites

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

 
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)