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July 3, 2010 16:58
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New England climate analysis, further addressing autocorrelation
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# Attempting to replicate analysis in: | |
# http://wattsupwiththat.com/2010/06/29/waxman-malarkey-impact-zone-us-northeast/ | |
# 7/3/2010: Nychka approach | |
# Data import and cleanup | |
# Note that 2010 is excluded due to missing values | |
dat <- read.table("~/Desktop/drd964x.tmpst.txt", colClasses=c("character",rep("numeric", 12))) | |
colnames(dat) <- c("id", "jan", "feb", "mar", "apr", "may", "jun", "jul", "aug", "sep", "oct", "nov", "dec") | |
dat$year <- as.numeric(substr(dat$id, 7, 10)) | |
dat <- dat[dat$year < 2010,] | |
dat$region <- substr(dat$id, 1, 3) | |
dat$annual <- apply(dat[,2:13], 1, mean) | |
dat.ne <- dat[dat$region == "101",] | |
# Ugliest possible way to average previous year's December | |
# and current year's January and February | |
dat.ne$last.dec <- (c(NA,dat.ne$dec))[1:115] | |
dat.ne$winter <- (dat.ne$jan + dat.ne$feb + dat.ne$last.dec) / 3 | |
# Create time series for autocorrelation analysis | |
ts.annual <- ts(dat.ne$annual, start=c(1895, 1), frequency=1) | |
ts.winter <- ts(dat.ne$winter[-1], start=c(1896, 1), frequency=1) | |
ts.annual.1970 <- window(ts.annual, start=1970) | |
ts.winter.1970 <- window(ts.winter, start=1970) | |
# Fit linear trends for full time series | |
fm <- function(ts) { | |
lm(ts ~ time(ts)) | |
} | |
fm.annual <- fm(ts.annual) | |
fm.annual.1970 <- fm(ts.annual.1970) | |
fm.winter <- fm(ts.winter) | |
fm.winter.1970 <- fm(ts.winter.1970) | |
# Plot residuals | |
par(mfrow=c(2,2)) | |
plot(residuals(fm.annual) ~ time(ts.annual),xlim=c(1895,2009)) | |
plot(residuals(fm.annual.1970) ~ time(ts.annual.1970)) | |
plot(residuals(fm.winter) ~ time(ts.winter),xlim=c(1895,2009)) | |
plot(residuals(fm.winter.1970) ~ time(ts.winter.1970)) | |
### Nychka analysis | |
nychka <- function(fm) { | |
output <- list() | |
# Calculate sample lag-1 autocorrelation | |
resids <- residuals(fm) | |
n <- length(resids) | |
rhohat <- cor(resids[2:n], resids[1:(n-1)]) | |
output$n <- n | |
output$rhohat <- rhohat | |
# See Nychka Eq. 5 | |
neff <- n * (1 - rhohat - 0.68 / sqrt(n)) / (1 + rhohat + 0.68 / sqrt(n)) | |
output$neff <- neff | |
# Calculate scaling for SE, see Nychka Eq. 3, 6 | |
sescale <- sqrt((n-2)/(neff-2)) | |
output$sescale <- sescale | |
# Calculate adjusted SE for warming trend | |
seadj <- sescale * sqrt(vcov(fm)[2,2]) | |
output$seadj <- seadj | |
# Calculate adjusted p-value | |
pval <- (1 - pt(coefficients(fm)[2] / seadj, neff)) * 2 | |
output$pval <- pval | |
output | |
} | |
print(nychka(fm.annual)) | |
print(nychka(fm.annual.1970)) | |
print(nychka(fm.winter)) | |
print(nychka(fm.winter.1970)) | |
### MLE analysis | |
require(nlme) | |
mle.ar1 <- function(ts) { | |
fm.trend <- gls(ts ~ time(ts), corr=corAR1(), method="ML") | |
fm.notrend <- gls(ts ~ 1, corr=corAR1(), method="ML") | |
print(anova(fm.trend, fm.notrend)) | |
} | |
mle.ar1(fm.annual) | |
mle.ar1(fm.annual.1970) | |
mle.ar1(fm.winter) | |
mle.ar1(fm.winter.1970) |
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