trend.test {aTSA}R Documentation

Trend Test


Performs an approximate Cox-Stuart or Difference-Sign trend test.


trend.test(x, method = c("cox.stuart", "diff.sign"), plot = FALSE)



a numeric vector or univariate time series.


test method. The default is method = "cox.stuart".


a logical value indicating to display the plot of data. The default is FALSE.


Cox-Stuart or Difference-Sign test is used to test whether the data have a increasing or decreasing trend. They are useful to detect the linear or nonlinear trend. The Cox-Stuart test is constructed as follows. For the given data x[1],...,x[t], one can divide them into two sequences with equal number of observations cutted in the midpoint and then take the paired difference, i.e., D = x[i] - x[i+c], i = 1, ..., floor(n/2), where c is the index of midpoint. Let S be the number of positive or negative values in D. Under the null hypothesis that data have no trend, for large n = length(x), S is approximately distributed as N(n/2,n/4), such that one can immediately obtain the p value. The exact Cox-Stuart trend test can be seen in cs.test of snpar package.

The Difference-Sign test is constructed as the similar way as Cox-Stuart test. We first let D = x[i] - x[i - 1] for i = 2, ..., n and then count the number of positive or negative values in D, defined as S. Under the null hypothesis, S is approximately distributed as N((n-1)/2,(n+1)/12). Thus, p-value can be calculated based on the null distribution.


A list with class "htest" containing the following components:

a character string giving the names of the data.


the type of test applied.


a character string describing the alternative hypothesis.


the p-value for the test.


the value of the test statistic with a name describing it.


Missing values are removed.


Debin Qiu


D.R. Cox and A. Stuart (1955). Some quick sign tests for trend in location and dispersion. Biometrika, Vol. 42, pp. 80-95.

P.J. Brockwell, R.A. Davis, Time Series: Theory and Methods, second ed., Springer, New York, 1991. (p. 37)


x <- rnorm(100)
trend.test(x,plot = TRUE) # no trend

x <- 5*(1:100)/100
x <- x + arima.sim(list(order = c(1,0,0),ar = 0.4),n = 100)
trend.test(x,plot = TRUE) # increasing trend

[Package aTSA version Index]