cobs (version 1.3-2)

globtemp: Annual Average Global Surface Temperature

Description

Time Series of length 113 of annual average global surface temperature deviations from 1880 to 1992.

Usage

data(globtemp)

Source

‘temp.data’ in file ‘cobs.shar’ available from http://www.cba.nau.edu/pin-ng/cobs.html.

Details

This is Example 1 of the COBS paper, where the hypothesis of a monotonely increasing trend is considered; Koenker and Schorfheide (1994) consider modeling the autocorrelations.

References

He, X. and Ng, P. (1999) COBS: Qualitatively Constrained Smoothing via Linear Programming; Computational Statistics 14, 315--337.

Koenker, R. and Schorfheide F. (1994) Quantile Spline Models for Global Temperature Change; Climate Change 28, 395--404.

Examples

data(globtemp)
plot(globtemp, main = "Annual Global Temperature Deviations")
str(globtemp)
## forget about time-series, just use numeric vectors:
year <- as.vector(time(globtemp))
temp <- as.vector(globtemp)



##---- Code for Figure 1a of He and Ng (1999) ----------

a50 <- cobs(year, temp, knots.add = TRUE, degree = 1, constraint = "increase")
summary(a50)
## As suggested in the warning message, we increase the number of knots to 9
a50 <- cobs(year, temp, nknots = 9, knots.add = TRUE, degree = 1,
            constraint = "increase")
summary(a50)
## Here, we use the same knots sequence chosen for the 50th percentile
a10 <- cobs(year, temp, nknots = length(a50$knots), knots = a50$knot,
            degree = 1, tau = 0.1, constraint = "increase")
summary(a10)
a90 <- cobs(year, temp, nknots = length(a50$knots), knots = a50$knot,
            degree = 1, tau = 0.9, constraint = "increase")
summary(a90)

which(hot.idx  <- temp >= a90$fit)
which(cold.idx <- temp <= a10$fit)
normal.idx <- !hot.idx & !cold.idx

plot(year, temp, type = "n", ylab = "Temperature (C)", ylim = c(-.7,.6))
lines(predict(a50, year, interval = "both"), col = 2)
lines(predict(a10, year, interval = "both"), col = 3)
lines(predict(a90, year, interval = "both"), col = 3)
points(year, temp, pch = c(1,3)[2 - normal.idx])

## label the "hot" and "cold" days
text(year[hot.idx], temp[hot.idx] + .03, labels = year[hot.idx])
text(year[cold.idx],temp[cold.idx]- .03, labels = year[cold.idx])