itam: Innovative Trend Analysis Method

In trend: Non-Parametric Trend Tests and Change-Point Detection

Innovative Trend Analysis Method

Description

The function performs the innovative trend analysis (ITA) method (Şen 2012).

Usage

itam(x, conf.level = 0.95)

Arguments

x	numeric vector or a time series object of class "ts"
conf.level	numeric, the level of significance

Details

The magnitude of trend is calculated based on the difference between the arithmeric means of the second half \bar{y} and the first half \bar{x} of the time series:

b = 2 ~ \left( \bar{y} - \bar{x} \right) / n,

with n the total number of observations in the full series.

The corresponding (corrected) standard deviation according to Serinaldi et al. (2020) is

\sigma_{b}^2 = \frac{16}{n^2} \frac{s^2}{n} \left(1 - \rho_{\bar{x}\bar{y}}\right),

with s^2 the variance of the full series and \rho_{\bar{x}\bar{y}} the correlation coefficient between the sample means of the sub-series (X) and (Y).

The test statistitic is:

z = b / \sigma_{b}.

The p-values are calculated from the standard normal distribution for the two-sided case.

For a critical review of the ITA method the reader is referred to Serinaldi et al. (2020).

Value

A list of class “htest” and “itam”.

estimates	numeric, ITAM slope
data.name	character string that denotes the input data
p.value	the p-value
statistic	the z quantile of the standard normal distribution
null.value	the null hypothesis
conf.in	upper and lower confidence limit
alternative	the alternative hypothesis
method	character string that denotes the test
df	A data.frame with ordered x1 and ordered x2

Note

Current Version is for complete observations only. For odd n the mid-point of the series is omitted.

References

Şen, Z. (2012) Innovative Trend Analysis Methodology. Journal of Hydrologic Engineering 17, 1042–1046. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1061/(ASCE)HE.1943-5584.0000556")}

Serinaldi, F., Chebana, F., Kilsby, C.G. (2020) Dissecting Innovative Trend Analysis. Stoch Environ Res Risk Assess 34, 733–754. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s00477-020-01797-x")}

Examples

(out <- itam(Nile))
plot(out)

## Not run: 
 # brief MC analysis, no trend, no autocorrelation, homoscedasticy
set.seed(1010)
xmat <- matrix(rnorm(30 * 1000), ncol = 1000, nrow = 30)
pvals <- sapply(seq_len(ncol(xmat)), function(j) itam(xmat[,j])$p.value)
# nominal error 0.05
sum(pvals < 0.05) / length(pvals)

## End(Not run)

trend documentation built on Oct. 24, 2026, 5:07 p.m.