Created
July 6, 2010 20:45
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Structural change analysis of HadCRUT3 annual time series data
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# Change-point analysis of HadCRUT3 annual time series data | |
require(strucchange) | |
# Data import | |
dat.raw <- read.table("~/Downloads/annual") | |
dat <- data.frame(temp=ts(dat.raw[,2], start=1850)) | |
dat <- window(cbind(temp=dat$temp, temp_lag1=lag(dat$temp, k = -1)), start=1851, end=2010) | |
# Structural change model | |
# Fit model | |
# Minimal segment size set to 5 years; overfit will be handled later | |
sc.alan <- breakpoints(temp ~ 1, h = 10, data=dat) | |
sc <- breakpoints(temp ~ time(temp), h = 5, data=dat) | |
sc.lag <- breakpoints(temp ~ time(temp) + temp_lag1 * time(temp), h = 5, data=dat) | |
plot(summary(sc.alan)) | |
plot(summary(sc)) | |
plot(summary(sc.lag)) | |
# Alan's model | |
# By inspecting the BIC, we select a model with 7 breaks | |
print(breakpoints(sc.alan, breaks=7)) | |
sc.alan <- lm(temp ~ breakfactor(sc.alan, breaks = 7), data=dat) | |
plot(dat[,1], ylab="temperature", main="Structural change model: no lag, 7 breakpoints") | |
lines(ts(fitted(sc.alan), start=1850), col=4) | |
lines(confint(sc.alan)) | |
# No red noise correction | |
# By inspecting the BIC, we select a model with 4 breaks | |
print(breakpoints(sc, breaks = 4)) | |
sc.4 <- lm(temp ~ time(temp) + breakfactor(sc, breaks = 4) * time(temp), data=dat) | |
plot(dat[,1],ylab="temperature",main="Structural change model: no lag, 4 breakpoints") | |
lines(ts(fitted(sc.4), start=1850), col=4) | |
lines(confint(sc)) | |
# Red noise correction | |
# By inspecting the BIC, we select a model with 1 break | |
print(breakpoints(sc.lag, breaks=1)) | |
sc.lag.1 <- lm(temp ~ time(temp) + breakfactor(sc.lag, breaks = 1) * time(temp), data=dat) | |
plot(dat[,1],ylab="temperature",main="Structural change model: 1 year lag, 1 breakpoint") | |
lines(ts(fitted(sc.lag.1), start=1851), col=4) | |
lines(confint(sc.lag)) | |
# Compare models | |
print(anova(sc.alan, sc.4, sc.lag.1)) |
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