Magnitude of trend in time series

Rand Wilcox has produced a set of functions for S-Plus and (IIRC) R, which
includes Theil-Sen regression.

The following url gives a pdf to the workshop that they were designed to
accompany, along with instructions on how to source and use them.

http://psychology.usc.edu/rwilcox/workshop.pdf 

The following url is to his homepage which gives the above link plus those
to the function files themselves.

http://psychology.usc.edu/faculty_homepage.php?id=43


HTH

Regards

Mike

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Barry Baker
Sent: 12 January 2007 23:48
To: r-help at stat.math.ethz.ch
Subject: [R] Magnitude of trend in time series

Hello,

I am analyzing some climate time series data using the Mann Kendall package
and was wondering if there was a way to calculate the trend using Sen's
nonparametric estimator slope in R?

Thank you in advance,
Barry
_________________________
Barry Baker, Ph.D.
Global Climate Change Initiative
The Nature Conservancy
2424 Spruce St., Suite 100
Boulder, CO 80302

Tel: (303)-541-0322
Fax: (303)-449-4328

http://nature.org/tncscience/scientists/misc/baker.html

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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

I am analyzing some climate time series data using the Mann Kendall package
and was wondering if there was a way to calculate the trend using Sen's
nonparametric estimator slope in R?

I think you can do it with the mblm package.  But I vaguely remember
that the results didn't look reasonable.  I've included some
simulation/testing code that I used below.

b1 <- 5
x <- 1:20 - mean(1:20)
y <- 0 + b1 * x

n1 <- function() y + rnorm(20, 0, 2)
ln1 <- function() y + log(rnorm(20, 0, 0.7))
ln2 <- function() y + log(rnorm(20, 0, 1.5))

fitlm <- function(f=n1) {
  m <- lm(n1() ~ x)
  ci <- t(sapply(c(0.9, 0.95, 0.99), function(x) confint(m, level=x)[2,]))
  b1 > ci[,1] & b1 < ci[,2]
}
fitts <- function(f=n1) {
  x <- x # because mblm mucks up the environments
  y2 <- n1()
  m <- mblm(y2 ~ x, repeated=FALSE)
  ci <- t(sapply(c(0.9, 0.95, 0.99), function(x) confint(m, level=x)[2,]))
  b1 > ci[,1] & b1 < ci[,2]
}

n1lm <- replicate(1000, fitlm(n1))
n1ts <- replicate(100, fitts(n1))
ln1lm <- replicate(1000, fitlm(ln1))
ln1ts <- replicate(100, fitts(ln1))
ln2lm <- replicate(1000, fitlm(ln2))
ln2ts <- replicate(100, fitts(ln2))


Hadley