Calculate local trends using cumsum

A simple method using cumulated sums that allows to detect changes in the tendency in a time series

local.trend(x, k=mean(x), plotit=TRUE, type="l", cols=1:2, ltys=2:1,
    xlab="Time", ylab="cusum", ...)
# S3 method for class 'local.trend'
identify(x, ...)

Arguments

x: a regular time series (a 'ts' object) for local.trend() or a 'local.trend' object for identify()
k: the reference value to substract from cumulated sums. By default, it is the mean of all observations in the series
plotit: if plotit=TRUE (by default), a graph with the cumsum curve superposed to the original series is plotted
type: the type of plot (as usual notation for this argument)
cols: colors to use for original data and for the trend line
ltys: line types to use for original data and the trend line
xlab: label of the x-axis
ylab: label of the y-axis
...: additional arguments for the graph

Details

With local.trend(), you can:

- detect changes in the mean value of a time series

- determine the date of occurrence of such changes

- estimate the mean values on homogeneous intervals

Value

a 'local.trend' object is returned. It has the method identify()

References

Ibanez, F., J.M. Fromentin & J. Castel, 1993. Application de la mÃ©thode des sommes cumulÃ©es Ã l'analyse des sÃ©ries chronologiques ocÃ©anographiques. C. R. Acad. Sci. Paris, Life Sciences, 316:745-748.

Author

Note

Once transitions are identified with this method, you can use stat.slide() to get more detailed information on each phase. A smoothing of the series using running medians (see decmedian()) allows also to detect various levels in a time series, but according to the median statistic. Under R, see also the 'strucchange' package for a more complete, but more complex, implementation of cumsum applied to time series.

Examples

data(bnr)
# Calculate and plot cumsum for the 8th series
bnr8.lt <- local.trend(bnr[,8])

# To identify local trends, use:
# identify(bnr8.lt)
# and click points between which you want to compute local linear trends...