library(Kendall)
library(mblm)

# the CO2 data has too much trend; Instead 
# Kendall library includes an example data set
#  of precipitation for the entire Great Lakes watershed
#  1900 - 1986


data(PrecipGL)

# PrecipGL is a time series, so it has a year attribute
PrecipGL

# which we can extract and store
precip.year <- time(PrecipGL)

# and a plot works nicely without an X variable
plot(PrecipGL)

# can convert to vectors
precip <- as.vector(PrecipGL)
precip.year <- as.vector(precip.year)

plot(precip.year,precip)

# Kendall's tau for any x and y
Kendall(precip.year,precip)

# or when obs are sequential over time
MannKendall(precip)

# if data are monthly (and only monthly)
# SeasonalMannKendall(X)

# Theil-Sen estimate of slope
library(mblm)
precip.theil <- mblm(precip~precip.year,repeated=F)

# have print, summary and confint methods
precip.theil
summary(precip.theil)
confint(precip.theil)

# use for data with a single dl value < any obs value
#  by replacing with all < dl values by some thing smaller
#  then any observed value.  Kendall correct, but Theil Sen approximate