Description Usage Details Source References Examples

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

1 |

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.

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

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | ```
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])
``` |

```
Time-Series [1:113] from 1880 to 1992: -0.32 -0.32 -0.4 -0.39 -0.65 -0.43 -0.4 -0.52 -0.3 -0.12 ...
qbsks2():
Performing general knot selection ...
WARNING! Since the number of 6 knots selected by AIC reached the
upper bound during general knot selection, you might want to rerun
cobs with a larger number of knots.
Deleting unnecessary knots ...
Searching for missing knots ...
WARNING! Since the number of 6 knots selected by AIC reached the
upper bound during general knot selection, you might want to rerun
cobs with a larger number of knots.
COBS regression spline (degree = 1) from call:
cobs(x = year, y = temp, constraint = "increase", degree = 1, knots.add = TRUE)
{tau=0.5}-quantile; dimensionality of fit: 4 from {4}
x$knots[1:4]: 1880, 1947, 1969, 1992
coef[1:4]: -0.4426198, 0.0200000, 0.0200000, 0.2960013
R^2 = 69.95% ; empirical tau (over all): 55/113 = 0.4867257 (target tau= 0.5)
qbsks2():
Performing general knot selection ...
Deleting unnecessary knots ...
Searching for missing knots ...
COBS regression spline (degree = 1) from call:
cobs(x = year, y = temp, constraint = "increase", nknots = 9, degree = 1, knots.add = TRUE)
{tau=0.5}-quantile; dimensionality of fit: 6 from {6}
x$knots[1:6]: 1880, 1908, 1936, ... , 1992
coef[1:6]: -0.40678101, -0.31185185, 0.02000000, 0.02000000, 0.06666667, 0.43641321
R^2 = 70.87% ; empirical tau (over all): 57/113 = 0.5044248 (target tau= 0.5)
COBS regression spline (degree = 1) from call:
cobs(x = year, y = temp, constraint = "increase", knots = a50$knot, nknots = length(a50$knots), degree = 1, tau = 0.1)
{tau=0.1}-quantile; dimensionality of fit: 6 from {6}
x$knots[1:6]: 1880, 1908, 1936, ... , 1992
coef[1:6]: -0.5515010, -0.4255000, -0.1400000, -0.1400000, -0.0800000, 0.1300034
empirical tau (over all): 12/113 = 0.1061947 (target tau= 0.1)
COBS regression spline (degree = 1) from call:
cobs(x = year, y = temp, constraint = "increase", knots = a50$knot, nknots = length(a50$knots), degree = 1, tau = 0.9)
{tau=0.9}-quantile; dimensionality of fit: 6 from {6}
x$knots[1:6]: 1880, 1908, 1936, ... , 1992
coef[1:6]: -0.2481832, -0.0700000, 0.1300000, 0.1300000, 0.2420000, 0.5080043
empirical tau (over all): 101/113 = 0.8938053 (target tau= 0.9)
[1] 10 21 22 36 47 58 59 61 68 74 101 102
[1] 5 8 25 38 39 71 77 85 86 92 97 113
```

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